Question

A debt of $1500 bearing at 12% compounded annually is to be discharged by the sinking fund method. If six annual deposits are made into a fund which pays 6% compounded monthly.

a. Find the annual interest payment
b. Find the size of the annual deposit into the sinking fund.
c. What is the annual cost of this debt?
d. Construct the sinking fund schedule.

Answer 1

The annual interest payment is $180. The size of the annual deposit into the sinking fund is approximately $116.53. The annual cost of this debt is $296.53.

Step-by-step explanation:

To calculate the annual interest payment:

Interest rate = 12%

Principal amount = $1500

Annual interest payment = Principal amount * Interest rate = $1500 * 12% = $180

To calculate the size of the annual deposit into the sinking fund:

Interest rate = 6% compounded monthly

Number of years = 6

Number of periods = Number of years * 12 = 6 * 12 = 72

Future value = $1500

$1500 = [Annual deposit * ((1 + (6%/12))^72 - 1)] / (6%/12)

After solving the equation, we find that the annual deposit into the sinking fund is approximately $116.53

To calculate the annual cost of this debt:

Annual cost = Annual interest payment + Size of the annual deposit into the sinking fund

Annual cost = $180 + $116.53 = $296.53

To construct the sinking fund schedule:

Year | Beginning Balance | Annual Deposit | Interest Earned | Ending Balance

1 | $0 | $116.53 | $0 | $116.53

2 | $116.53 | $116.53 | $8.88 | $241.94

3 | $241.94 | $116.53 | $17.75 | $376.22

4 | $376.22 | $116.53 | $27.84 | $520.60

5 | $520.60 | $116.53 | $39.78 | $677.91

6 | $677.91 | $116.53 | $54.12 | $849.56