A $145,000 loan is repaid over 10 years using the sinking fund method.The sinking fund earns interest at j₂ = 6%,while the interest rate on the loan is j₂ = 8%.What is the semi-annual expense of debt?

Question

Quizplus · Accepted Answer

Using the sinking fund method, we need to find the semi-annual payment that would repay the loan in 10 years, and also accumulate enough money in the sinking fund to pay off the loan. Let X be the semi-annual payment, and Y be the amount we deposit in the sinking fund each period.

The loan balance after n periods is:
B(n) = 145000*(1.04)^n - X*(1.04^n-1)/0.04

The sinking fund balance after n periods is:
S(n) = Y*((1.03)^n-1)/0.03

At the end of the 10th year, the sinking fund should be able to pay off the loan balance, so we have:
S(20) = 145000

Also, each period, the sinking fund should earn enough interest to cover the interest on the loan, so we have:
Y*0.03 >= X*0.02

Combining these equations and solving for X, we get:
X = $11,196.28

Therefore, the semi-annual expense of debt is $11,196.28. The answer is B.

A $145,000 Loan Is Repaid Over 10 Years Using the Sinking