Introduction

In this lesson, you will find the total cost of a loan given the payment information. When a loan is paid off using monthly payments, more is paid than the loan was originally worth because of interest. To calculate how much the loan costs in total, multiply the monthly payment by the number of payments made.

This video illustrates the lesson material below. Watching the video is optional.

• Total Cost of Loan Given Payment (4:09 mins) | Transcript

Total Cost of Loan Given Payment

The total cost of a loan is equal to all of the payments that you make added together over the course of the loan.

\begin{align*} Total\;Cost = Monthly\;Payment\times Total\;Number\;of\;Payments \end{align*}

Remember, within each payment is both the principal amount and the interest being charged on that loan, so the total cost of the loan is the amount that was borrowed plus the total interest being paid on that loan.

Example 1
Calculate the total cost of a loan with a $300 monthly payment over seven years.

Paying monthly for 7 years means there are 84 total payments. This is because there are 12 months in a year: \(12\times7=84\).

To calculate the total cost of the loan, multiply the monthly payment times the total number of payments:

\begin{align*} 84\times \$300 = \$25,200 \end{align*}

This amount of $25, 000 is the total amount of the loan. It is the amount of the principal plus the interests that will be paid for 7 years.

Using Microsoft Excel to Calculate the Total Cost of a Loan

To do the same calculations using Microsoft Excel, type the needed information into cells and then use a formula that includes multiplication.

• Type Payments into cell A1 and 300 into cell B1.
• Type Years into cell A2 and 7 into cell B2.
• Type Total Cost into cell A4 and a formula in cell B4 that uses cell references. The formula should multiply the Payments (in cell B1) by the Years (In cell B2) and by 12 since the payment is monthly. The formula will look like this: =B1*B2*12.

Figure 1

• Press Enter

Figure 2

It’s important to understand how to calculate the total cost of the loan because the total cost of the loan can be very different depending on the payment and the length of the loan in years. If you are considering getting a loan, don't be tempted to accept it just on the amount of the monthly payment. Understand the total cost of the loan before you make a decision.

Things to Remember

• To calculate the total loan cost, multiply the monthly payment by the number of payments made.
  \begin{align*} Total\;Cost = Monthly\;Payment\times Total\;Number\;of\;Payments \end{align*}

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

   x

   Solution: \($1074 \times 30 \times 12 = $386,640\)
   
   Details:
   When finding the total cost of a loan, start by finding the following:
   
   Monthly payment amount: \({\color{Red}$1074}\)
   
   Number of years you pay the payment: \({\color{Purple}30}\)
   
   Number of times per year that you pay the payment: \({\color{Blue}12}\)
   Note: This is 12 because you make monthly payments.
   
   The total cost = \(({\color{Red}{\text{monthly payment}}})\) times \(({\color{Purple}{\text{number of years}}})\) times \(({\color{Blue}{\text{number of times per year that you make the payment}}})\)
   
   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

   x

   Solution: \($367 \times 5 \times 12 = $22,020\)
   
   Details:
   When finding the total cost of a loan, start by finding the following:
   
   Monthly payment amount: \({\color{Red}$367}\)
   
   Number of years you pay the payment: \({\color{Purple}5}\)
   
   Number of times per year that you pay the payment: \({\color{Blue}12}\)
   Note: This is 12 because you make monthly payments.
   
   The total cost = \(({\color{Red}{\text{monthly payment}}})\) times \(({\color{Purple}{\text{number of years}}})\) times \(({\color{Blue}{\text{number of times per year that you make the payment}}})\)
   
   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

   x

   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

   x

   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

   x

   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

   x

   Solution: \($1850 \times 10 \times 12 = $222,000\)
   )

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