ACT Math - 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?

$4.80

$12.00

$24.00

$48.00

$32.00

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

What interest is expected to be paid on a loan for $55,000 with 3% interest compounded annually over a period of 6 years?

Explanation

The simple interest formula is,

$P\left ( 1+rY\right )$ where is the principal, is th rate of interest, and is the number of years. So,

$55\textup{,}000(1+.03\left ( 6\right ))=64\textup{,}900$

$64\textup{,}900-55\textup{,}000=9900$

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?

$9000

$6000

$3000

$12,000

$1500

Explanation

Simple interest = Amount borrowed x Interest rate =

150,000 x 6% = 150,000 x .06 = $9000

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:

$p = \frac{3125}{(.05)(5)} = $ 12500$

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:

$t = \frac{2325}{(.0155)(5000)} = 30$

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.

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 .

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:

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:

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?