# ACT Math : Interest

## Example Questions

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### Example Question #1 : Interest

Ben and Sam are starting a furniture design business. In order to build their shop, they borrow $150,000 from their neighborhood bank. The interest rate on the loan is 6%. How much interest do they have to pay? Possible Answers:$1500

$6000$3000

$9000$12,000

$9000 Explanation: Simple interest = Amount borrowed x Interest rate = 150,000 x 6% = 150,000 x .06 =$9000

### Example Question #1 : How To Find Simple Interest

Amy recently opened a new credit card. In her first month, expenditures totaled $500 and she was not charged any interest. Amy paid$80 from her first month's bill. The second month, Amy spent another $60 on her credit card. This time, she was charged 5% interest on her total unpaid balance. How much interest was Amy charged? Possible Answers:$24.00

$32.00$4.80

$48.00$12.00

$24.00 Explanation: This requires us to keep track of Amy's expenses. After her first month, the unpaid balance was 500 - 80 =$420.

However, after the second month, her unpaid balance went up to $480. 5% of 480 can be obtained by multiplying 480 x .05 = 24 ### Example Question #1 : How To Find Simple Interest Ella loaned Frances$10,000 to start a business. They agreed that the loan would be paid back in five years, with a simple interest rate of 9%. When the loan is paid back in full, what will be the total amount that Ella collects?

Explanation:

The simple interest formula is given by I = PRt where I = interest, P = principal, R = rate, and t = time.

Here, I = 10,000 * 0.09 * 5 = $4,500. The total repayment amount is the interest plus the principal, so$4,500 + $10,000 =$14,500 total repayment.

### Example Question #1 : How To Find Simple Interest

An account accrues  of simple interest during a fifteen year period. If this is accrued yearly at a rate of , what was the initial balance of the account at the beginning of this period? Round to the nearest dollar.

Explanation:

Simple interest has the formula of:

, where  is the starting balance,  is the interest rate, and  is the number of accrual periods.

For our data, this is simply:

Simplifying, we get:

Divide both sides by  to get:

### Example Question #5 : How To Find Simple Interest

An account accrues simple interest on an initial balance of  dollars at a rate of  per year. After  years, how much interest has accrued to the account?

Explanation:

Simple interest has the formula of:

, where  is the starting balance,  is the interest rate, and  is the number of accrual periods.

For our data, this is simply:

### Example Question #6 : How To Find Simple Interest

The equation  can be used to calculate simple interest, where  is the total interest,  is the principal amount,  is the rate of interest expressed as a decimal and  is the amount of times interest is added.

A man pays  in annual interest on a loan of . If the loan repayment term was  years, what was the interest rate?

Explanation:

Plugging our variables into the above equation gives us

Thus, our interest rate is .

### Example Question #7 : How To Find Simple Interest

The equation  can be used to calculate simple interest, where  is the total interest,  is the principal amount,  is the rate of interest expressed as a decimal and  is the amount of times interest is added.

Grant takes out a personal loan to buy a car. He pays  in interest before the loan is repaid. If the interest rate is  compounded annually and it took Grant  years to repay the loan, what amount was the original loan for?

Explanation:

Using the  equation gives us:

### Example Question #8 : How To Find Simple Interest

The equation  can be used to calculate simple interest, where  is the total interest,  is the principal amount,  is the rate of interest expressed as a decimal and  is the amount of times interest is added.

Ashley wants to take out a loan for some home improvements. She knows that her simple interest rate will be  monthly, and that she will need to borrow . If she wants to pay no more than  in interest over the life of the loan, what is the longest amount of time in months she has to pay off the loan?

Explanation:

Using the  equation gives us:

### Example Question #9 : How To Find Simple Interest

The equation  can be used to calculate simple interest, where  is the total interest,  is the principal amount,  is the rate of interest expressed as a decimal and  is the amount of times interest is added.

A loan officer realizes an error has been committed on an account -- a customer with a  loan has been paying an annual interest rate of  for the last  years instead of the promised annual interest rate of . If the loan was just paid off, how much money does the bank owe the customer?

Explanation:

First, we must use our formula to determine how much money the customer has paid in interest:

Now, calculate how much should have been paid, based on the correct interest rate:

Lastly, find the difference between these two numbers:

Thus, the bank owes the customer .

### Example Question #10 : How To Find Simple Interest

How much more money will a savings account at  annual simple interest generate than an account at , if both accounts start with  and are left untouched for  years?