Question

A small town is going to build a new facility for which the town has planned and saved for the past 7 years. The facility will cost $150,000.The town has saved the full cost of this project by starting a savings account (Sinking Fund) earning interest at 4.5% per year compounded biannually. 1. What were the regular biannual payments made by the town to save the money in 7 years? 2. What is the total amount that the town paid to save the necessary amount? The contractors offer to build the same facility for another town at the same price. However this town has not planned for the facility and has to borrow the money from a bank at 4.5% per year compounded biannually and to be paid off in 7 years. 3. What would be the size of the regular biannual payments the town has to make to pay the loan in 7 years? 4. What will be the total amount the town has to pay to retire the loan?

Answer 1

1.

Biannual interest rate R = 4.5%/2 = 2.25%

Time n = 14 biannual period

Future value of the savings = $150000

Let, biannual deposits for the saving = P

Then,

150000 = P*(1.0225^14 – 1)/.0225

150000 = P*16.2437

P = 150000/16.2437

P = $9234.35

So, regular biannual payment will be $9234.35 to save $150000 in 7 years.

2.

Total amount paid by the town to save the funds = 14*$9234.35

Total amount paid by the town to save the funds = $129280.9

3.

If loan of $150000 is taken,

Biannual interest rate R = 4.5%/2 = 2.25%

Time n = 14 biannual period

Let, biannual instalments = P

Then,

150000 = P*(1-1/1.0225^14)/.0225

150000 = P*11.8959

P = 150000/11.8959

P = $12609.39

So, biannual payment will be $12609.39.

4.

Total amount to be paid = 14*12609.39 = $176531.5