Question

Peter wants to borrow $3,000. He has two payment plans to choose from. Plan A charges 4% interest over 6 years. Plan B charges 5% interest over 4 years. The formula mc024-1.jpg can be used to calculate the monthly payment, m, where P is the principle amount borrowed, r is the interest rate expressed as a decimal, and t is the time of the loan, in years. Which statement best compares the plans?
Plan A has a monthly payment of about $23 less and a total interest charge of $120 less than plan B.
Plan A has a monthly payment of about $23 less and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 less than plan B.

Answer 1

Use the simple-interest monthly-payment formula m = P(1 + rt)/(12t).

Plan A: P = 3000, r = 0.04, t = 6
- Total repaid = 3000(1 + 0.04·6) = 3000(1.24) = $3,720
- Monthly mA = 3720/72 = $51.67
- Interest = 3720 − 3000 = $720

Plan B: P = 3000, r = 0.05, t = 4
- Total repaid = 3000(1 + 0.05·4) = 3000(1.20) = $3,600
- Monthly mB = 3600/48 = $75.00
- Interest = 3600 − 3000 = $600

Comparison: Plan A’s monthly payment is about $23.33 less, and Plan A’s total interest is $120 more than Plan B. So the second statement is correct.