After doing a complex amortization calculation to find the payment, we often will calculate how much

interest a borrower pays over the life of the loan. One thing we need to find first is how much the borrower

pays back in total $($then we can subtract the principal$).$

This calculation is very simple compared with the amortization formula! We just multiply the payment by

the number of payments made.

For example, if the monthly payments are $$300,$ and the loan is $18$ years, then the total amount the

borrower pays back, which includes principal and interest, is just:

$(\frac{\text{\$}300}{\text{m}\text{o}\text{n}\text{t}\text{h}})(\frac{12\text{m}\text{o}\text{n}\text{t}\text{h}\text{s}}{\text{y}\text{e}\text{a}\text{r}})(\frac{18\text{y}\text{e}\text{a}\text{r}\text{s}}{1})=$$$64800$

Find the total amount the borrower pays $($principal and interest$)$ in each case below:

The payments are $$235$ per month for $60$ months $($a $5$ year loan$)$:

The payments are $$1254$ per month for $30$ years: