Question

The town of Mount Hope is financing a $4.5 million upgrade to its water system though the province’s Municipal Finance Authority (MFA). The MFA obtained financing via a bond issue with interest at 7.5% compounded semi-annually. At the end of every 6 months, the town is to make equal payments into a sinking fund administered by the MFA so that the necessary funds will be available to repay the $4.5 million bond when it matures in 20 years. The sinking fund earns 4% compounded semi-annually. a. Determine the semi-annual interest payments made to the bond holders. b. Determine the amount of the sinking fund payments. c. Determine the semi-annual expense of the debt to the town of Mount Hope.

Answer 1

a)

semi annual payments = 4,500,000 *(7.5% / 2) = $168,750

b)

this can be solved using future value of annuity formula

future value of annuity = P*[(1+r)^n - 1 / r ]

where , P = semi annual payments

r = rate per period = 4% / 2 = 2%

n = number of periods = 20 x 2 = 40

4500000 = P*[(1+2%)^40 - 1 / 2% ]

P = 4500000 / 60.40198

P = $74500.87

sinkingfund payments = $74500.87

c)

semi annual expenses of the debt = interest payments + sinking fund payments

= 168750 + 74500.87

= $243,250.87