Question

A loan of 1000 is taken out at an annual effective interest rate of 5%. The loan will be repaid using the Sinking Fund Method. That is, level annual interest payments are made at the end of each year for 10 years, and the principal amount for the loan is repaid at the end of 10 years by making equal size payments into the fund at the end of each year for 10 years.
If the sinking fund earns an annual effective interest rate of 4%, then find the difference between the interest payment on the loan and the interest earned by the sinking fund in the fifth year. Round your answer to the nearest whole number.

Answer 1

Answer:

Interest paid each year = 5% of 1000 = $50

$1000 is to be paid at the end of 10 years.So payment each year = pmt(rate,nper,pv,fv) where rate = 0.04,nper=10 and fv =1000.

Payment into the fund =pmt(0.04,10,0,1000) = $83.29 each year

Value of the sinking fund at the end of the 4th year =pv(rate,nper.pmt) =pv(0.04,4,83.29) = 302.34

Interest earned by sinking fund in year 5 = 0.04*302.34 = 12.09

Interest on loan in 5th year = $50

So difference between the interest payment on the loan and the interest earned by the sinking fund in the fifth year. = 50-12.09 = 37.91 = $38 (to nearest whole number)