Question

a business owner receives a $5,000 loan with 13% interest, charged at the end of each year.

1. select an equation to represent the amount owed, in dollars, after the given number of years of making no payments after t years.

$y = 5000(1.13)^t$
$y = 5000(13)^t$
$y = 1.13(5000)^t$
$y = 5000(0.83)^t$
$y = 5000(0.13)^t$

Explanation:

Step1: Identify growth type

This is compound annual growth, so use the compound interest formula for annual compounding: $A = P(1 + r)^t$, where $P$ is principal, $r$ is annual interest rate, $t$ is time in years.

Step2: Plug in given values

Principal $P = 5000$, annual interest rate $r = 0.13$. Substitute into the formula:
$y = 5000(1 + 0.13)^t = 5000(1.13)^t$

Step3: Match to options

The derived equation matches the first option.

Answer:

A. $y = 5000(1.13)^t$