Interest - ACT Math
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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?
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?
Simple interest = Amount borrowed x Interest rate =
150,000 x 6% = 150,000 x .06 = $9000
Simple interest = Amount borrowed x Interest rate =
150,000 x 6% = 150,000 x .06 = $9000
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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?
An account accrues simple interest on an initial balance of
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:
Simple interest has the formula of:
For our data, this is simply:
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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?
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?
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
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
Compare your answer with the correct one above
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?
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?
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.
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.
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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.
An account accrues
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:
Simple interest has the formula of:
For our data, this is simply:
Simplifying, we get:
Divide both sides by
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What interest is expected to be paid on a loan for $55,000 with 3% interest compounded annually over a period of 6 years?
What interest is expected to be paid on a loan for $55,000 with 3% interest compounded annually over a period of 6 years?
The simple interest formula is,
where 
is the principal, 
is th rate of interest, and 
is the number of years. So,
The simple interest formula is,
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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?
The equation
A man pays
Plugging our variables into the above equation gives us
Thus, our interest rate is 
.
Plugging our variables into the above equation gives us
Thus, our interest rate is
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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?
The equation
Grant takes out a personal loan to buy a car. He pays
Using the 
equation gives us:
Using the
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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?
The equation
Ashley wants to take out a loan for some home improvements. She knows that her simple interest rate will be
Using the 
equation gives us:
Using the
Compare your answer with the correct one above
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?
The equation
A loan officer realizes an error has been committed on an account -- a customer with a
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 
.
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
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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?
How much more money will a savings account at
First, we must use our formula to determine how much interest each account generates, then subtract the greater from the smaller.
So, the account at 
interest saves 
more.
First, we must use our formula to determine how much interest each account generates, then subtract the greater from the smaller.
So, the account at
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A credit union pays out interest to its members proportional to their contributions to savings accounts at the end of each financial year in which the union posts a profit. If at the end of the year, the credit union posts a profit of 
, and Antoine contributed 
to his savings account when the year ended, how much interest is he entitled to?
A credit union pays out interest to its members proportional to their contributions to savings accounts at the end of each financial year in which the union posts a profit. If at the end of the year, the credit union posts a profit of
If the profit was 
and the contributions were 
, then we can use the equation 
, where 
is the principal, 
is the rate and 
is the number of periods of time interest is applied (in this case, 
since this is a one-time payout).
Thus, Antoine is entitled to 
in interest.
If the profit was
Thus, Antoine is entitled to
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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?
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?
Simple interest = Amount borrowed x Interest rate =
150,000 x 6% = 150,000 x .06 = $9000
Simple interest = Amount borrowed x Interest rate =
150,000 x 6% = 150,000 x .06 = $9000
Compare your answer with the correct one above
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?
An account accrues simple interest on an initial balance of
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:
Simple interest has the formula of:
For our data, this is simply:
Compare your answer with the correct one above
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?
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?
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
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
Compare your answer with the correct one above
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?
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?
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.
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.
Compare your answer with the correct one above
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.
An account accrues
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:
Simple interest has the formula of:
For our data, this is simply:
Simplifying, we get:
Divide both sides by
Compare your answer with the correct one above
What interest is expected to be paid on a loan for $55,000 with 3% interest compounded annually over a period of 6 years?
What interest is expected to be paid on a loan for $55,000 with 3% interest compounded annually over a period of 6 years?
The simple interest formula is,
where is the principal, is th rate of interest, and is the number of years. So,
The simple interest formula is,
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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?
The equation
A man pays
Plugging our variables into the above equation gives us
Thus, our interest rate is .
Plugging our variables into the above equation gives us
Thus, our interest rate is
Compare your answer with the correct one above
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?
The equation
Grant takes out a personal loan to buy a car. He pays
Using the equation gives us:
Using the
Compare your answer with the correct one above