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

For the contractor:
Simple interest rate = 12%
Time = 7 months
Interest earned = P x r x t
where P is the principal = $750,000
r is the rate = 0.12
t is the time in years = 7/12
Interest earned = 750,000 x 0.12 x 7/12 = $52,500

For the small business:
Compound interest rate = 12% compounded monthly
Time = 7 months
Interest earned = P(1 + r/n)^(n*t) - P
where P is the principal = $750,000
r is the annual interest rate = 0.12
n is the number of times the interest is compounded in a year = 12
t is the time in years = 7/12
Interest earned = 750,000(1 + 0.12/12)^(12*7/12) - 750,000 = $54,101.51

Therefore, the bank should lend the money to the small business for the additional interest earned of $54,101.51 - $52,500 = $1601.51.

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