### Home > CC3 > Chapter 9 > Lesson 9.1.3 > Problem 9-37

9-37.

Joaquin has agreed to lend his younger brother $45 so that he can buy a new tank for his pet lizard. Homework Help ✎

Joaquin is charging his brother 2% simple interest per month. If his brother pays him back in 6 months, how much will Joaquin get back?

If Joaquin’s brother instead borrowed the money from a bank at 2% compound interest per month, how much would he have to pay the bank at the end of 6 months?

Using the equation for simple interest:

Interest = *Prt* *P* = principal *r* = interest rate *t* = time

Interest = $45(.02)(6 months)

$50.40

Remember, the total money Joaquin gets back includes the principal and the interest.

Use the equation for compound interest:

Total Amount = *P*(1 + *r*)^{n}*P* = principal*r* = rate

*n* = number of times compounded