A business needs a $240,000 loan for one year and has two options to

Official Explanation

First, find the interest rate at which the two options have equal total interest payments.

Interest on Loan 1:

5% of $240,000 = 0.05 × $240,000 = $12,000

Alternatively, find 10% and divide by 2 to get 5%: 10% of 240,000 = 24,000. Half of that is 12,000.

Interest on Loan 2:

4% of $190,000 = 0.04 × $190,000 = $7,600

r% of \($50,000=\frac{r}{100}×$50,000=$500r\)

For the total interest payment on Option 1 to be equal to the total interest payment on Option 2, the sum of the interest on the $50,000 loan and the interest on the $190,000 loan must be equal to the interest payment on the $240,000 loan. Set up that equation and solve.

500r + 7,600 = 12,000

500r = 12,000 – 7,600

500r = 4,400

r = 8.8

Next, calculate the interest rate at which the interest payment on the $190,000 loan (at 4%) would be equal to twice the interest payment on the $50,000 loan (at r%). Reuse the numbers already calculated during the first half of this problem.

interest on 190k loan = 2(interest on 50k loan)

7,600 = 2(500r)

7,600 = 1,000r

r = 7.6

Column 1: The correct answer is (E).
Column 2: The correct answer is (D).