DSQ: Calculating compound interest - GMAT Quantitative

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, 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 $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.

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 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.

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 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.

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:

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, 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 $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.

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 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.

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 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.

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:

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, 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 $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.