Question

name
lesson quiz
3-6

1. vince borrows $900 to buy a couch. he will pay off the loan by paying 1.5% simple interest for 2 years. vince incorrectly calculates the amount he will pay back using the expression below.

$900 + 900(1.015 • 2)$
what is the correct amount vince will pay back altogether? explain the error in vinces expression.

Explanation:

Step1: Recall simple interest formula

Simple interest: $I = P \cdot r \cdot t$, where $P=\$900$, $r=0.015$, $t=2$

Step2: Calculate total repayment

Total = Principal + Interest: $A = P + P \cdot r \cdot t$

Step3: Substitute values and compute

$A = 900 + 900(0.015 \cdot 2)$
$A = 900 + 900(0.03)$
$A = 900 + 27$

Answer:

The correct amount Vince will pay back is $\$927$.
Vince's error was using $1.015$ (which is $1 + 0.015$, the factor for annual growth in compound interest) instead of the decimal form of the simple interest rate, $0.015$. Simple interest uses the raw interest rate, not the rate plus 1, to calculate interest owed.