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 1 year.

$y = 5000(13)^1$
$y = 5000(0.83)^1$
$y = 5000(1.13)^1$
$y = 5000(0.13)^1$
$y = 1.13(5000)^1$

Explanation:

Step1: Understand compound interest basics

When interest is added annually, the total amount owed after \(t\) years is calculated using the formula \(y = P(1 + r)^t\), where \(P\) is the principal amount, \(r\) is the annual interest rate (in decimal form), and \(t\) is time in years.

Step2: Identify given values

Here, \(P = 5000\), \(r = 0.13\) (13% converted to decimal), and \(t = 1\).

Step3: Substitute values into formula

Substitute the values into the formula: \(y = 5000(1 + 0.13)^1 = 5000(1.13)^1\)

Answer:

\(y = 5000(1.13)^1\)