Question

A company borrowed $45,000 for 3 years at 5% compounded monthly. It will NOT make any payments on this loan prior to maturity. (a) Find the total future value the company will need to accumulate to pay off this debt. Show all work. (b) Use the result of part (a) to find the quarterly sinking fund payment needed to accumulate this maturity value (over the the 3 years), assuming 4% rate. show all work

Answer 1

Solution:

a)Calculation of future value of $45000

Future Vaue=Prsent Value-(1+Interest Rate/no. of compounding)^no. of years*no. of compounding

=$45000(1+0.05/12)^3*12

=$45,000*1.16417

=$52,387.65

Thus,company will need to accumulate $52,387.65 pay off the debt.

b)Caculation of quarterly sinking fund payment

Annuity=Future value/[(1+rate/no. of compunding)^no. of years*no. of compunding]-1/(rate/no. of compounding)

=$52,387.65/[(1+0.04/4)^3*4]-1/(0.04/4)

=$52,387.65/12.68250

=$4130.70

Thus the quarterly sinking fund payment is $4130.70