Question

Problem. A company borrowed $4,250,000 at an effective rate of 4.25% for 5 years. To make sure it has the money needed to repay the loan when it comes due, the company is making deposits into a sinking fund at the beginning of each quarter. The sinking fund pays the company 3.21%. (a) How much will the company need to have at maturity to pay off this loan? (b) How much should each sinking fund payment be? You must show detailed calculations to receive credit for your answers.

Answer 1

(a)

Borrowed Amount(P) = $4,250,000

Effective interest rate(i) = 4.25%

Term in years(n) = 5

Amount to be paid off at maturity of loan = F

$\large F = \$523,322.31$

(b)

Deposit to sinking fund at beginning of each quarter = A

Interest rate = 3.21%

Quarterly interest rate (i) = 0.0321/4 = 0.008025

No. of quarterly deposit in 5 years (n) = 5*4 = 20

Required amount at end of 5th year (F) = $523,322.31

Thus,

$A = F*\left ( \frac{i}{(1+i)^n-1} \right )*\frac{1}{(1+i)}$

$A = 523,322.31*\left ( \frac{0.008025}{(1+0.008025)^{20}-1} \right )*\frac{1}{(1+0.008025)}$

by solving,

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.