Interest Problems - GMAT Quantitative
Card 1 of 136
Today, I put 
in a bank account which promises me a fixed interest rate for 
years. How much simple interest (in dollars) have I earned after 
years?
(1) I have 
in my bank account after year 
.
(2) The annual interest rate is 
.
Today, I put
(1) I have
(2) The annual interest rate is
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From statement (1), we can get the annual interest rate:
.
Therefore after year 2 the simple interest is:
. So statement (1) alone is sufficient.
Statement (2) gives us the annual interest rate directly so we can get the result by simply applying the simple interest formula:
. So statement (2) alone is sufficient.
Therefore the right answer is D.
From statement (1), we can get the annual interest rate:
Therefore after year 2 the simple interest is:
Statement (2) gives us the annual interest rate directly so we can get the result by simply applying the simple interest formula:
Therefore the right answer is D.
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John invests 
in bonds and certificates. The bonds earn 
interest per year. The certificates earn 
interest per year. At the end of the year, John earns a total of 
as interest. What amount of money did John invest in bonds?
(1) The ratio of interest earned from the certificates to the interest earned from the bonds is 
.
(2) The total interest earned 
.
John invests
(1) The ratio of interest earned from the certificates to the interest earned from the bonds is
(2) The total interest earned
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Statement (1) is not very helpful. Since we do not know the total amount of interest earned or at least the interest earned from one of the financial products (either the bonds or the certificates), we cannot determine the original amount invested in either product.
Using Statement(2), we can set the following equation:
(Let x be the amount invested in bonds)
John invested $4200 in bonds and $7800 in certificates.
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
Statement (1) is not very helpful. Since we do not know the total amount of interest earned or at least the interest earned from one of the financial products (either the bonds or the certificates), we cannot determine the original amount invested in either product.
Using Statement(2), we can set the following equation:
(Let x be the amount invested in bonds)
John invested $4200 in bonds and $7800 in certificates.
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
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What amount of money did John invest at 8% simple interest?
(1) The amount of interest earned on this investment in one year is $400.
(2) John's investment is supposed to accumulate to 7,000 after 5 years.
What amount of money did John invest at 8% simple interest?
(1) The amount of interest earned on this investment in one year is $400.
(2) John's investment is supposed to accumulate to 7,000 after 5 years.
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(1) The amount of interest earned on this investment in one year is $400.
Let X be the amount invested. The simple annual interest rate is 8%.
The amount of money John invested is $5000. Statement (1) Alone is sufficient.
(2) John's investment is supposed to accumulate to 7,000 after 5 years.
Let X be the amount invested. The simple annual interest rate is 8%.
The amount of money John invested is $5000. Statement (2) Alone is sufficient.
(1) The amount of interest earned on this investment in one year is $400.
Let X be the amount invested. The simple annual interest rate is 8%.
The amount of money John invested is $5000. Statement (1) Alone is sufficient.
(2) John's investment is supposed to accumulate to 7,000 after 5 years.
Let X be the amount invested. The simple annual interest rate is 8%.
The amount of money John invested is $5000. Statement (2) Alone is sufficient.
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Jake invests $5000 at 10% simple annual interest and another amount of money at 
percent simple interest. What amount of money did Jake invests at 
percent interest?
(1) The total amount of interest earned on all investments at the end of one year is $800.
(2) 
.
Jake invests $5000 at 10% simple annual interest and another amount of money at
(1) The total amount of interest earned on all investments at the end of one year is $800.
(2)
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(1) The total amount of interest earned on all investments at the end of one year is $800.
Let A be the amount of money invested at x percent. The total interest earned on both investments is:
We cannot calculate A because x is also unknown. Statement (1) Alone is not sufficient then.
(2) x=6%
Statement (2) Alone is not sufficient.
Combining both statements, we have:
Both Statements together are sufficient but neither statement alone is sufficient.
(1) The total amount of interest earned on all investments at the end of one year is $800.
Let A be the amount of money invested at x percent. The total interest earned on both investments is:
We cannot calculate A because x is also unknown. Statement (1) Alone is not sufficient then.
(2) x=6%
Statement (2) Alone is not sufficient.
Combining both statements, we have:
Both Statements together are sufficient but neither statement alone is sufficient.
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Jennifer's grandmother opens up a savings account for her that draws simple interest. No one adds to or withdraws from the account until Jennifer's 18th birthday.
Will there be $10,000 in the account by the time Jennifer turns 18?
Statement 1: Jennifer's grandmother opened the account the day Jennifer turned five years old.
Statement 2: The account pays 4.5% simple interest.
Jennifer's grandmother opens up a savings account for her that draws simple interest. No one adds to or withdraws from the account until Jennifer's 18th birthday.
Will there be $10,000 in the account by the time Jennifer turns 18?
Statement 1: Jennifer's grandmother opened the account the day Jennifer turned five years old.
Statement 2: The account pays 4.5% simple interest.
Tap to reveal answer
Simple interest can be calculated using the formula
where 
is the principal, or amount deposited; 
is the interest rate, expressed as a decimal; and 
is the time, expressed in years.
The question is whether the total of the original principal and the accrued interest will be at least $10,000, or, whether
or
is true or false.
Assume both statements. From Statement 1, we get that 
, and from Statement 2, we get that 
. However, neither statement gives the value of principal 
, so the two statements together are insufficient to answer the question.
Simple interest can be calculated using the formula
where
The question is whether the total of the original principal and the accrued interest will be at least $10,000, or, whether
or
is true or false.
Assume both statements. From Statement 1, we get that
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On January 2, Grant uses his $5,000 inheritance to open up a savings account that pays simple interest; he does not add to or withdraw from the account. How many years does it take for the account to be worth $6,000?
Statement 1: The account pays 4.5% annually.
Statement 2: The interest rate of his savings account is 2% less than that of his certificate of deposit in the same bank.
On January 2, Grant uses his $5,000 inheritance to open up a savings account that pays simple interest; he does not add to or withdraw from the account. How many years does it take for the account to be worth $6,000?
Statement 1: The account pays 4.5% annually.
Statement 2: The interest rate of his savings account is 2% less than that of his certificate of deposit in the same bank.
Tap to reveal answer
Simple interest can be calculated using the formula
where 
is the principal, or amount deposited; 
is the interest rate, expressed as a decimal; and 
is the time, expressed in years. Since the main body of the problem gives that Grant deposited $5,000 and that the amount of interest to be earned is
,
the equation becomes
Therefore, all that is needed to calculate 
is the interest rate of the account. Statement 1 gives this explicitly. Statement 2 is irrelevant, as it only compares the interest rate to that of another account, which is not given.
Simple interest can be calculated using the formula
where
the equation becomes
Therefore, all that is needed to calculate
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On the same day, Robin and Rick each open a savings account that draws simple interest. Neither withdraws from or deposits into his or her account over the next five years. Throughout the five-year period, whose account accrues more interest?
Statement 1: Both accounts pay the same interest rate.
Statement 2: Robin deposited $400 more than Rick.
On the same day, Robin and Rick each open a savings account that draws simple interest. Neither withdraws from or deposits into his or her account over the next five years. Throughout the five-year period, whose account accrues more interest?
Statement 1: Both accounts pay the same interest rate.
Statement 2: Robin deposited $400 more than Rick.
Tap to reveal answer
Simple interest can be calculated using the formula
where 
is the principal, or amount deposited; 
is the interest rate, expressed as a decimal; and 
is the time, expresssed in years. For both accounts, 
, so the amount of interest earned will be
Neither statement alone gives sufficient information; Statement 1 alone compares the interest rates but not the amounts of principal, and the reverse holds true for Statement 2.
Assume both statements. The accounts pay the same interest rate, which we will continue to call 
; however, the principal Robin deposited, which we will call 
, is greater than that deposited by Rick, which we will call 
. Therefore,
That is, Robin's account accrues more interest.
Simple interest can be calculated using the formula
where
Neither statement alone gives sufficient information; Statement 1 alone compares the interest rates but not the amounts of principal, and the reverse holds true for Statement 2.
Assume both statements. The accounts pay the same interest rate, which we will continue to call
That is, Robin's account accrues more interest.
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On the same day, Grace and Shannon each open a savings account that draws simple interest. Neither withdraws from or deposits into her account over the next five years. Throughout the five-year period, whose account accrues more interest?
Statement 1: Grace's account pays at a rate of 1% per year more than Shannon's account.
Statement 2: Grace deposited $5,000 in her account.
On the same day, Grace and Shannon each open a savings account that draws simple interest. Neither withdraws from or deposits into her account over the next five years. Throughout the five-year period, whose account accrues more interest?
Statement 1: Grace's account pays at a rate of 1% per year more than Shannon's account.
Statement 2: Grace deposited $5,000 in her account.
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Assume both statements together. If we let 
be the interest rate, as a decimal, for Grace's account, the amount of interest Grace's account accrues over five years is
The interest rate of Shannon's account is 
, so, if we let 
be amount she deposited in her account, the amount of interest Shannon's account accrued is
Without any information about how much Shannon deposited, or about the actual interest rates, it is impossible to determine which is the greater.
Assume both statements together. If we let
The interest rate of Shannon's account is
Without any information about how much Shannon deposited, or about the actual interest rates, it is impossible to determine which is the greater.
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Marshall's grandfather uses $7,000 to open up a savings account for him that draws simple interest. No one adds to or withdraws from the account until Marshall's 21st birthday.
Will there be $10,000 in the account by the time Marshall turns 21?
Statement 1: The account pays 3.8% simple interest.
Statement 2:Marshall's grandfather opened the account the day Marshall turned six years old.
Marshall's grandfather uses $7,000 to open up a savings account for him that draws simple interest. No one adds to or withdraws from the account until Marshall's 21st birthday.
Will there be $10,000 in the account by the time Marshall turns 21?
Statement 1: The account pays 3.8% simple interest.
Statement 2:Marshall's grandfather opened the account the day Marshall turned six years old.
Tap to reveal answer
Simple interest can be calculated using the formula
where is the principal, or amount deposited; is the interest rate, expressed as a decimal; and is the time, expressed in years.
The question is whether the total of the original principal and the accrued interest will be at least $10,000. Since this makes 
, the question becomes whether
or
is true or false.
Statement 1 and Statement 2 each give the value of only one of the two variables—Statement 1 gives that 
and Statement 2 gives that 
—but neither gives the other value. The two together, however, allow us to substitute for both variables and test the inequality for truth:
This statement is true, so the savings account will indeed accrue to a value above $10,000 by Marshall's 21st birthday.
Simple interest can be calculated using the formula
where
The question is whether the total of the original principal and the accrued interest will be at least $10,000. Since this makes
or
is true or false.
Statement 1 and Statement 2 each give the value of only one of the two variables—Statement 1 gives that
This statement is true, so the savings account will indeed accrue to a value above $10,000 by Marshall's 21st birthday.
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Jenna needs 
years from today to start a business. After talking to an investment banker, Jenna is assured to gain an annually compounded interest of 
.
What amount of money does Jenna need to invest today?
(1) 
(2) 
Jenna needs
What amount of money does Jenna need to invest today?
(1)
(2)
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Using statement (1), the value of i cannot be determined because t is not specified.
Therefore Statement (1) ALONE is not sufficient.
Using statement (2), the value of i can be determined:
We can then set the following equation with X being the amount of money Jenna has to invest today:
We calculate X as follows:
Using statement (1), the value of i cannot be determined because t is not specified.
Therefore Statement (1) ALONE is not sufficient.
Using statement (2), the value of i can be determined:
We can then set the following equation with X being the amount of money Jenna has to invest today:
We calculate X as follows:
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At the beginning of January of 2015, Olga invested one half of the money she earned in December of 2014 in a certificate of deposit that pays 3.15% annual interest, compounded monthly. At the end of six years, how much will that certificate of deposit be worth?
Statement 1: Olga earned $63,000 in 2014.
Stateent 2: Olga earned the same amount of money each month in 2013.
At the beginning of January of 2015, Olga invested one half of the money she earned in December of 2014 in a certificate of deposit that pays 3.15% annual interest, compounded monthly. At the end of six years, how much will that certificate of deposit be worth?
Statement 1: Olga earned $63,000 in 2014.
Stateent 2: Olga earned the same amount of money each month in 2013.
Tap to reveal answer
In order to know how much money is in an account after compound interest is accrued, one thing that must be known is the principal, or amount invested.
Statement 2 is unhelpful, since information from 2013 is not relevant to information for 2014.
From Statement 1 we only know her 2014 earnings, not her December earnings (it is not given that she earned the same per month in 2014). Therefore, the two statements together provide insufficient information.
In order to know how much money is in an account after compound interest is accrued, one thing that must be known is the principal, or amount invested.
Statement 2 is unhelpful, since information from 2013 is not relevant to information for 2014.
From Statement 1 we only know her 2014 earnings, not her December earnings (it is not given that she earned the same per month in 2014). Therefore, the two statements together provide insufficient information.
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Natasha decides to invest her entire Christmas bonus in a certificate of deposit that pays 2.15% annual interest, compounded monthly. At the end of five years, how much will that certificate of deposit be worth?
Statement 1: Natasha was given a $3,000 Christmas bonus.
Stateent 2: Natasha earns an annual salary of $54,000.
Natasha decides to invest her entire Christmas bonus in a certificate of deposit that pays 2.15% annual interest, compounded monthly. At the end of five years, how much will that certificate of deposit be worth?
Statement 1: Natasha was given a $3,000 Christmas bonus.
Stateent 2: Natasha earns an annual salary of $54,000.
Tap to reveal answer
In order to know how much money is in an account after compound interest is accrued, the following must be known:
The amount of principal, which is given as $3,000 (Natasha's Christmas bonus) only in Statement 1;
The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;
The frequency with which the interest is compounded, which is given as monthly in the main body of the problem; and,
The rate of interest, which is given as 2.15% in the main body of the problem.
Statement 1 alone provides sufficient information to allow the answer to be calculated. Statement 2 is irrelevant, since it provides no information about Natasha's Christmas bonus.
In order to know how much money is in an account after compound interest is accrued, the following must be known:
The amount of principal, which is given as $3,000 (Natasha's Christmas bonus) only in Statement 1;
The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;
The frequency with which the interest is compounded, which is given as monthly in the main body of the problem; and,
The rate of interest, which is given as 2.15% in the main body of the problem.
Statement 1 alone provides sufficient information to allow the answer to be calculated. Statement 2 is irrelevant, since it provides no information about Natasha's Christmas bonus.
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Mitchell deposits an amount of money in a savings account that pays compound interest. He does not deposit or withdraw during that time. How much money does he have at the end of five years?
Statement 1: Mitchell deposited $10,000.
Statement 2: The savings account draws annual interest of 2.12%, compounded quarterly.
Mitchell deposits an amount of money in a savings account that pays compound interest. He does not deposit or withdraw during that time. How much money does he have at the end of five years?
Statement 1: Mitchell deposited $10,000.
Statement 2: The savings account draws annual interest of 2.12%, compounded quarterly.
Tap to reveal answer
In order to know how much money is in an account after compound interest is accrued, the following must be known:
The amount of principal, which is given as $10,000 only in Statement 1;
The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;
The frequency with which the interest is compounded, which is given as quarterly only in Statement 2; and,
The rate of interest, which is given as 2.12% only in Statement 2.
Therefore, both statements together are necessary and sufficient to answer the question.
In order to know how much money is in an account after compound interest is accrued, the following must be known:
The amount of principal, which is given as $10,000 only in Statement 1;
The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;
The frequency with which the interest is compounded, which is given as quarterly only in Statement 2; and,
The rate of interest, which is given as 2.12% only in Statement 2.
Therefore, both statements together are necessary and sufficient to answer the question.
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John deposits an amount of money in a savings account that pays compound interest. He does not deposit or withdraw during that time. How much money does he have at the end of five years?
Statement 1: John deposited $5,000.
Statement 2: The interest is compounded monthly.
John deposits an amount of money in a savings account that pays compound interest. He does not deposit or withdraw during that time. How much money does he have at the end of five years?
Statement 1: John deposited $5,000.
Statement 2: The interest is compounded monthly.
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Assume both statements are known.
In order to know how much money is in an account after compound interest is accrued, the following must be known:
The amount of principal, which is stated to be $5,000 in Statement 1;
The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;
The frequency with which the interest is compounded, which is given to be monthly in Statement 2; and,
The rate of interest, which is not given anywhere.
Insufficient information is given.
Assume both statements are known.
In order to know how much money is in an account after compound interest is accrued, the following must be known:
The amount of principal, which is stated to be $5,000 in Statement 1;
The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;
The frequency with which the interest is compounded, which is given to be monthly in Statement 2; and,
The rate of interest, which is not given anywhere.
Insufficient information is given.
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Joe invests $4,000 in a certificate of deposit that accrues interest that is compounded monthly. What is the annual interest rate?
Statement 1: During the first month, the certificate drew $7.83 in interest.
Statement 2: During the second month, Joe drew $7.85 in interest.
Joe invests $4,000 in a certificate of deposit that accrues interest that is compounded monthly. What is the annual interest rate?
Statement 1: During the first month, the certificate drew $7.83 in interest.
Statement 2: During the second month, Joe drew $7.85 in interest.
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Assume Statement 1 alone is true.
If 
is the annual interest rate, in its decimal form, of a $4,000 CD that draws $7.83 interest in the first month, then
This is a linear equation in one variable that can be solved for 
.
Assume Statement 2 is true. Then the equation becomes
This is a quadratic equation in one variable that can be solved for 
.
Either way, the annual interest rate can be found, so either statement alone is sufficient.
Assume Statement 1 alone is true.
If
This is a linear equation in one variable that can be solved for
Assume Statement 2 is true. Then the equation becomes
This is a quadratic equation in one variable that can be solved for
Either way, the annual interest rate can be found, so either statement alone is sufficient.
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Tyler invests $20,000 in a certificate of deposit that draws compound interest. How frequently is the interest compounded - monthly, bimonthly, or quarterly?
Statement 1: The certificate draws 3.15% annual compound interest.
Statement 2: The certificate draws $638.33 the first year.
Tyler invests $20,000 in a certificate of deposit that draws compound interest. How frequently is the interest compounded - monthly, bimonthly, or quarterly?
Statement 1: The certificate draws 3.15% annual compound interest.
Statement 2: The certificate draws $638.33 the first year.
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The compound interest equation is
where 
is the value at the end of the period in question, 
is the principal, or initial investment, 
is the interest rate in decimal form, 
is the number of times the interest is compounded per year, and 
is the number of years.
We know 
from the main body of the problem. It is known that 
only if Statement 1 is knwon, and it is known that 
only if Statement 2 is known. Also, 
can only be deduced from Statement 2:
Therefore, neither statement alone is sufficient. If both statements are assumed true, the equation becomes
or, dividing both sides by 20,000,
The question can be answered by substituting 4 (quarterly), 6 (bimonthly), and 12 (monthly) in turn and seeing which one makes the above statement true.
The compound interest equation is
where
We know
Therefore, neither statement alone is sufficient. If both statements are assumed true, the equation becomes
or, dividing both sides by 20,000,
The question can be answered by substituting 4 (quarterly), 6 (bimonthly), and 12 (monthly) in turn and seeing which one makes the above statement true.
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Quincy invests $30,000 in a certificate of deposit that draws compound interest. How frequently is the interest compounded - monthly, bimonthly, or quarterly?
Statement 1: The first interest payment is 0.964% of the principal.
Statement 2: The first interest payment is $289.20
Quincy invests $30,000 in a certificate of deposit that draws compound interest. How frequently is the interest compounded - monthly, bimonthly, or quarterly?
Statement 1: The first interest payment is 0.964% of the principal.
Statement 2: The first interest payment is $289.20
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The two statements are equivalent, since 0.964% of $30,000 is
Therefore, it can be determined that the interest rate 0.964% is per compounding period. However, no clue is given as to how many compounding periods there are - for example, the annual interest rate is unknown. The two statements together provide insufficient information.
The two statements are equivalent, since 0.964% of $30,000 is
Therefore, it can be determined that the interest rate 0.964% is per compounding period. However, no clue is given as to how many compounding periods there are - for example, the annual interest rate is unknown. The two statements together provide insufficient information.
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Jenna needs years from today to start a business. After talking to an investment banker, Jenna is assured to gain an annually compounded interest of .
What amount of money does Jenna need to invest today?
(1)
(2)
Jenna needs
What amount of money does Jenna need to invest today?
(1)
(2)
Tap to reveal answer
Using statement (1), the value of i cannot be determined because t is not specified.
Therefore Statement (1) ALONE is not sufficient.
Using statement (2), the value of i can be determined:
We can then set the following equation with X being the amount of money Jenna has to invest today:
We calculate X as follows:
Using statement (1), the value of i cannot be determined because t is not specified.
Therefore Statement (1) ALONE is not sufficient.
Using statement (2), the value of i can be determined:
We can then set the following equation with X being the amount of money Jenna has to invest today:
We calculate X as follows:
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At the beginning of January of 2015, Olga invested one half of the money she earned in December of 2014 in a certificate of deposit that pays 3.15% annual interest, compounded monthly. At the end of six years, how much will that certificate of deposit be worth?
Statement 1: Olga earned $63,000 in 2014.
Stateent 2: Olga earned the same amount of money each month in 2013.
At the beginning of January of 2015, Olga invested one half of the money she earned in December of 2014 in a certificate of deposit that pays 3.15% annual interest, compounded monthly. At the end of six years, how much will that certificate of deposit be worth?
Statement 1: Olga earned $63,000 in 2014.
Stateent 2: Olga earned the same amount of money each month in 2013.
Tap to reveal answer
In order to know how much money is in an account after compound interest is accrued, one thing that must be known is the principal, or amount invested.
Statement 2 is unhelpful, since information from 2013 is not relevant to information for 2014.
From Statement 1 we only know her 2014 earnings, not her December earnings (it is not given that she earned the same per month in 2014). Therefore, the two statements together provide insufficient information.
In order to know how much money is in an account after compound interest is accrued, one thing that must be known is the principal, or amount invested.
Statement 2 is unhelpful, since information from 2013 is not relevant to information for 2014.
From Statement 1 we only know her 2014 earnings, not her December earnings (it is not given that she earned the same per month in 2014). Therefore, the two statements together provide insufficient information.
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Natasha decides to invest her entire Christmas bonus in a certificate of deposit that pays 2.15% annual interest, compounded monthly. At the end of five years, how much will that certificate of deposit be worth?
Statement 1: Natasha was given a $3,000 Christmas bonus.
Stateent 2: Natasha earns an annual salary of $54,000.
Natasha decides to invest her entire Christmas bonus in a certificate of deposit that pays 2.15% annual interest, compounded monthly. At the end of five years, how much will that certificate of deposit be worth?
Statement 1: Natasha was given a $3,000 Christmas bonus.
Stateent 2: Natasha earns an annual salary of $54,000.
Tap to reveal answer
In order to know how much money is in an account after compound interest is accrued, the following must be known:
The amount of principal, which is given as $3,000 (Natasha's Christmas bonus) only in Statement 1;
The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;
The frequency with which the interest is compounded, which is given as monthly in the main body of the problem; and,
The rate of interest, which is given as 2.15% in the main body of the problem.
Statement 1 alone provides sufficient information to allow the answer to be calculated. Statement 2 is irrelevant, since it provides no information about Natasha's Christmas bonus.
In order to know how much money is in an account after compound interest is accrued, the following must be known:
The amount of principal, which is given as $3,000 (Natasha's Christmas bonus) only in Statement 1;
The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;
The frequency with which the interest is compounded, which is given as monthly in the main body of the problem; and,
The rate of interest, which is given as 2.15% in the main body of the problem.
Statement 1 alone provides sufficient information to allow the answer to be calculated. Statement 2 is irrelevant, since it provides no information about Natasha's Christmas bonus.
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