SAT Math : How to find simple interest

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : How To Find Simple Interest

Dan took out a $1200 loan at a rate of 3% simple interest a year. What is the amount of interest accrued for one month?

Possible Answers:

Correct answer:

Explanation:

$1200 is the amount that he took out.

3% annually would yield an interest amount of $36.

Therefore, each month, he would be paying $3 a month.

Example Question #2 : How To Find Simple Interest

Peter wanted to buy a car and borrowed $2,500 from the bank at 5% simple interest per year.  He was able to pay back the loan in one lump sum at six months.  What was the total amount he paid the bank?

Possible Answers:

\$2750.25

\$3000

\$2625.50

\$2562.50

\$3250.75

Correct answer:

\$2562.50

Explanation:

Simple interest is given by i=prt where i = interest, p = principal, r = rate, and t = time in years.

i=2500\cdot (0.05)(0.5)=\$62.50

Remember, six months is the same as half of a year.  The total paid back to the bank is the principle plus the interest, or $2,562.50.

Example Question #3 : How To Find Simple Interest

I have $100 in my bank. After one year, I have withdrawn a total of $20 and I still have $85 in the bank. What is the yearly interest rate of my bank account?

Possible Answers:

Correct answer:

Explanation:

Since I have withdrawn $20, that means I only have $80 in my account.

 imples that

which is 6.25%.

Example Question #1 : How To Find Simple Interest

You really want to buy a car that costs $15,000 but you only have $5,000 saved. Rather than getting a bank loan, your parents offer to lend you the extra money but will require you to pay them back with 4.3% interest. How much will car cost in total after you have paid your parents back?

Possible Answers:

Correct answer:

Explanation:

Amount borrowed = $15,000  $5,000 = $10,000

Interest of 4.3% = $10,000 * 0.043 = $430

Total cost of car = $5000 + $10000 + $430 = $15,430

Example Question #2 : How To Find Simple Interest

Ted works over the summer and makes $9 per hour.  He works for 20 hours each week for 10 weeks.  After paying 10% in taxes, he buys a bike for $500 and puts the rest of his money in the bank.

If Ted's bank pays 5% interest on the total sum once per year, and Ted doesn't add or remove anything from the account, how much money (rounded to the nearest cent) will Ted have in 5 years?

Possible Answers:

Correct answer:

Explanation:

To start, we see that Ted works for 20 hours per week for 10 weeks.  This means he works a total of 200 hours over the summer.  He is paid $9 dollars each hour.  Therefore he makes $9 x 200 hours = $1800 total over the summer.  He then has to pay 10% in taxes, or .1 x $1800, leaving him with .  He buys the bike for $500, so he has $1620 - $500 = $1,120 to deposit at the bank.

Now we have to find out how much he will have 5 years later.  Since the bank pays 5% interest each year, we know that he will make 5% of what he has each year.  He starts with $1,120.  5% of this value is .  Adding this to the original $1,120 gives us $1,176.

This is also the same as multiplying instead by 1.05.  We repeat this step 5 times, giving us:

Example Question #2 : How To Find Simple Interest

A student puts  in the bank every year for years. If the account has a simple interest rate of  per year, how much money will the student have at the end of the first year?

Possible Answers:

Correct answer:

Explanation:

Simple interest is calculated using the following formula:

Where

future value

= present value

= interest rate

For this problem, that means:

Example Question #4 : How To Find Simple Interest

Andrew received  for his fifteenth birthday. He invested some of the money in an investment account and some of the money in a savings account. Both accounts accrue simple interest. The investment account has an interest of , while the savings account has an interest rate of .

At the end of the year, Andrew earned a total of  in interest. How much money did he put in each account?

Possible Answers:

 in the investment account and  in the savings account

 in the investment account and  in the savings account

 in the investment account and  in the savings account

 in the investment account and  in the savings account

 in the investment account and  in the savings account

Correct answer:

 in the investment account and  in the savings account

Explanation:

Step 1: Set up the system of equations. Simple interest means that interest is calculated at the end of the year. Therefore, the amount of interest at the end of the year is the amount invested times the interest rate.

Let  = the amount put in the investment account

Let  = the amount put in the savings account

Step 2: Use substitution to solve the system.

Substitute  for  in the second equation and solve for :

 

Step 3: Solve for :

Example Question #8 : How To Find Simple Interest

You invest $1000 in a bank that gives 5% interest every year on the money in your account. How much interest do you make in 3 years (to the nearest dollar)?

Possible Answers:

Correct answer:

Explanation:

Step 1: We need to convert  percent into a decimal. To do this, we need to move the decimal place back two spots.

. We move the decimal back two spots. The decimal starts right after the .

Step 2: Calculate Simple interest and ending balance for 1 year.

Interest=
Ending Balance=.

Step 3: Calculate Simple interest and ending balance for the next year (2nd year)

Interest=
Ending Balance= 

Step 4: Calculate Simple Interest and ending balance of the third and final year
Interest=
Ending Balance=

Step 5: Add up the interest calculations:

. Over three years, the account gained $158 in interest.

Example Question #5 : How To Find Simple Interest

If a student borrows $200,000 at an interest rate of 6% compounded annually, when she graduates in 4 years how much money will she owe? Round to the nearest dollar.

Possible Answers:

Correct answer:

Explanation:

This problem requires knowledge of the compound interest formula, 

Where  is the amount of money owed,  is the sum borrowed,  is the yearly interest rate,  is the amount of times the interest is compounded per year, and  is the number of years.  

We know that the student borrowed $200,000 compounded annually at a 6% interest rate, therefore by plugging in those numbers we find that after she graduates in 4 years she will owe $252,495.

Example Question #10 : How To Find Simple Interest

If a student borrows $200,000 at an interest rate of 6% compounded quarterly, when she graduates in 4 years how much money will she owe? Round to the nearest dollar.

Possible Answers:

Correct answer:

Explanation:

This problem requires knowledge of the compound interest formula, 

Where  is the amount of money owed,  is the sum borrowed,  is the yearly interest rate,  is the amount of times the interest is compounded per year, and  is the number of years.  

We know that the student borrowed $200,000 compounded quarterly at a 6% interest rate, therefore by plugging in those numbers we find what she will owe after she graduates in 4 years.

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