### Home > ACC7 > Chapter 9 Unit 10 > Lesson CC3: 9.1.3 > Problem9-37

9-37.

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

1. 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?

Using the equation for simple interest:

$\text{Interest} = Prt$
$P = \text{principal}$
$r = \text{interest rate}$
$t = \text{time}$

$\text{Interest} = 45(.02)(6 \text{ months})$

$50.40$

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

2. 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?

Use the equation for compound interest:

$\text{Total Amount} = P(1 + r)^{n}$
$P = \text{principal}$
$r = \text{rate}$
$n = \text{number of times compounded}$

$45(1+.02)^6=45\cdot 1.02^6=50.68$