Use the table to solve the problem. Round to the nearest cent.
-A bank has $550,000 to lend for 9 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 and what is the additional interest earned?
A)Contractor; $2,029.50
B)Business; $2,029.50
C)Business; $925,694.00
D)Contractor; $14,470.50

Question

Use the table to solve the problem. Round to the nearest cent. 
-A bank has $550,000 to lend for 9 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 and what is the additional interest earned?
A)Contractor; $2,029.50 
B)Business; $2,029.50 
C)Business; $925,694.00 
D)Contractor; $14,470.50

Quizplus · Accepted Answer

To find out which option would give the bank the most interest earned, we need to calculate the interest earned by each option.

Option 1: Lend to contractor at a simple interest rate of 12%.

The interest earned would be:

I = Prt
I = $550,000 x 0.12 x 0.75

Here, we used 0.75 because 9 months is 0.75 of a year (since 12 months is one year).

I = $49,500

Option 2: Lend to small business at a compound interest rate of 12% per year, compounded monthly.

We know that the principal is $550,000 and the interest rate is 12% per year. We also know that the loan will be for 9 months, or 0.75 of a year. To calculate the interest earned, we can use the following formula:

A = P(1 + r/n)^(nt)

Where:

A = the total amount of money earned (principal + interest)
P = the principal (the amount of money lent)
r = the interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years) that the money is invested

Plugging in our numbers, we get:

A = $550,000(1 + 0.12/12)^(12 x 0.75)
A = $575,695.50

So the interest earned would be:

I = A - P
I = $575,695.50 - $550,000
I = $25,695.50

Comparing the two options, we can see that the small business option would give the bank more interest earned ($25,695.50) than the contractor option ($49,500). Therefore, the bank should lend the money to the small business and the additional interest earned would be $25,695.50 - $49,500 = $-23,804.50 (negative means less than earned in the first option).

Use the Table to Solve the Problem