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Find the Total Cost of a Loan Given the Payment Information
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When we pay off a loan using monthly payments, we pay more than the loan was originally worth because of interest. To calculate how much the loan costs in total, we multiply the monthly payment and the number of payments made. The following video will show an example of this and how to calculate it using Excel.

Total Cost of Loan Given Payment

Total cost = Monthly payment × Total number of payments

### Practice Problems

1. If you pay $$1074$$ each month on your home mortgage for 30 years, how much will you pay in total for the home? (
Solution
Solution:
$$1074 \times 30 \times 12 = 386,640$$
Details:
When finding the total cost of a loan we start by finding the following:

Monthly payment amount: $${\color{Red}1074}$$

Number of years we pay the payment: $${\color{Purple}30}$$

Number of times per year that we pay the payment: $${\color{Blue}12}$$
Note: This is 12 because we make monthly payments.

The total cost = $$({\color{Red}{\text{monthly payment}}})$$ times $$({\color{Purple}{\text{number of years}}})$$ times $$({\color{Blue}{\text{number of times per year that we make the payment}}})$$

Total cost = ($${\color{Red}1074}$$)($${\color{Purple}30}$$)($${\color{Blue}12}$$)

Total cost = $$386,640$$
)
2. If you pay $$367$$ each month for five years to buy your car, how much is the total cost of the loan on the car? (
Solution
Solution:
$$367 \times 5 \times 12 = 22,020$$
Details:
When finding the total cost of a loan we start by finding the following:

Monthly payment amount: $${\color{Red}367}$$

Number of years we pay the payment: $${\color{Purple}5}$$

Number of times per year that we pay the payment: $${\color{Blue}12}$$
Note: This is 12 because we make monthly payments.

The total cost = $$({\color{Red}{\text{monthly payment}}})$$ times $$({\color{Purple}{\text{number of years}}})$$ times $$({\color{Blue}{\text{number of times per year that we make the payment}}})$$

Total cost = ($${\color{Red}367}$$)($${\color{Purple}5}$$)($${\color{Blue}12}$$)

Total cost = $$22,020$$
)
3. If you pay $$27.52$$ each month for your cell phone for two years, how much is the total cost of your cell phone? (
Solution
Solution:
$$27.52 \times 2 \times 12 = 660.48$$
)
4. If you pay your friend $$12$$ each month for nine months to repay a loan, what is the total cost of the loan? (
Solution
Solution:
$$12 \times 9 = 108$$
)
5. If you pay the credit card company $$59.75$$ each month in order to pay off your credit card, and it takes you 68 months to pay it off, what is the total cost of the credit card loan? (
Solution
Solution:
$$59.75 \times 68 = 4063$$
)
6. If you have a small business loan and you pay $$1850$$ each month for 10 years on the loan, what is the total cost of the loan? (
Solution
Solution:
$$1850 \times 10 \times 12 = 222,000$$
)

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