Question

The municipality of kirkland borrowed 130000 to build a recreation center. The debt principal is to be repaid in eight years, and interest is at 10.5% compounded annually is to be paid annually with end of year payments. To provide for the retirement of the debt the municipal council set up a sinking fund into which equal payments are made at the time of annual interest payments. Interest earned by the fund is 8% compounded annually.

What is annual interest payment on debt.

What is the annual payment into the sinking fund?

What is the total annual cost ( the periodic cost) of the debt?

Compute the book value of the debt after two years.

Compute the interest earned by the fund in year 5.

Answer 1

1)$P=S(i+\frac{i}{(1+i)^n-1})$

$P=130 000(0.105+\frac{0.105}{(1+0.105)^8-1})=24813.01$

2) the annual payment into the sinking fund is 24813.01

3)$the total annual cost ( the periodic cost) of the debt=24813.01\times8=198504.05$

4)$the book value of the debt after two years=198504.05-24813.01\times2=148 878.04$

5)this is an annuity

$FV=A(\frac{(1+r)^n-1}{r})$

A=24813.01

r=0.08

n=5

$FV=24813.01(\frac{(1+0.08)^5-1}{0.08})=145568$

$145568-24813.01\times5=21502.97$