Solve the problem. Round to the nearest cent as needed.
-A bank has $750,000 to lend for 7 months. It can lend it to a local contractor at a simple interest rate of 12%, or it can lend it to a small business that will pay 12% compounded monthly. If the bank wants to maximize its
Interest earned, who should receive the loan (contractor or business) and what is the additional interest earned?
A) Contractor; $52,500
B) Business; $1601.51
C) Contractor; $1601.51
D) Business; $54,101.51

Question

Quizplus · Accepted Answer

To maximize interest, the bank should lend to the business because compound interest yields more than simple interest over time. The additional interest earned is calculated by comparing the total interest from both options. For simple interest (contractor): Interest = Principal × Rate × Time = $750,000 × 12% × (7/12) = $52,500. For compound interest (business): Interest = Principal × (1 + Rate/n)^(nt) - Principal = $750,000 × (1 + 0.12/12)^(12*(7/12)) - $750,000 ≈ $54,101.51. The additional interest with compounding is $54,101.51 - $52,500 = $1,601.51.

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