Question

Your company borrows $275,000 today to fund its growth initiatives. it must repay the bank in five annual payments of $76,300 at the end of each year. what annual interest rate is your firm paying? group of answer choices

-18.02 percent
-10.85 percent
-12.01 percent
-17.75 percent

Answer 1

The annual interest rate your firm is paying for the $275,000 loan, repaid in five annual installments of $76,300, is approximately 12.01 percent.

Option c is correct.

The problem can be solved using the Present Value (PV) formula:

PV = PMT * (1 - (1 / (1 + r)^n)) / r

Where:

PV is the present value of the loan ($275,000)

PMT is the annual payment ($76,300)

n is the number of payments (5 years)

r is the annual interest rate (unknown)

We need to rearrange the formula to solve for r:

r = (1 - (PV / PMT)) / (1 - (1 / (1 + r)^n))

Plugging in the values:

r = (1 - (275,000 / 76,300)) / (1 - (1 / (1 + r)^5))

Solving for r using iterative methods (like trial and error or numerical solvers) gives the answer:

r ≈ 12.01%

Therefore, your firm is paying an annual interest rate of approximately 12.01%.

Option c is correct.