Melissa wants to buy a living room set that cost $1800. She could get a 3-year personal loan from a bank at a simple interest rate of 8.7%. She could also get a 3-year loan from a finance company that charges 8.5% compounded annually. Which answer correctly compares the total cost of the loan with simple interest and the loan with compound interest?

The total cost of the loan with simple interest $2269.8 is less than the loan with compound interest $2299.12.

Explanation:

Simple Interest (I) = Principal (Loan) * Time*Rate : 100

Loan = $1800

Time = 3 years

Rate = 8.7%

I = 1800*3*8.7/100 = $469.8

Total cost of loan with simple Interest = loan + simple interest = $1800 + $469.8 = $2269.8

Compound interest = [Loan (1+r) ^n] - Loan

Loan = $1800

r is annual interest rate = 8.5% = 0.085

n is duration of the loan = 3 years

Compound interest = [1800 (1+0.085) ^3] - 1800 = 2299.12 - 1800 = $499.12

Loan with compound interest = 1800 + 499.12 = $2299.12