Question

a) When you establish a sinking fund, which interest rate is better? 7% or 8% b) If you set up a sinking fund, which interest rate is better? 4% compounded semi-annual or 4% compounded quarterly

Answer 1

A sinking fund is a fund established by periodically setting aside funds either for repayment of a liability of the replacement of an asset.

In other words, a sinking fund is the future value of a series of periodical payments.

Future Value = Annuity x Future Value Interest Factor of an Annuity = Annuity x [ ( 1 + r) ⁿ - 1 ] / r

From the given formula, it is clear that the future value of an annuity would be higher if the interest rate is higher, or a smaller deposit would be needed to be made if the higher interest rate is opted for, the number of deposits n remaining the same.

a. 8% would be better from the point of the investor. It means a smaller deposit would suffice to reach the desired future sum.

b. 4% compounded semi-annual is better as the effective rate of interest is higher.

Effective rate of interest for 4% compounded semi-annually = ( 1 + 0.04 / 2 ) ² - 1 = 0.0404 or 4.04 %.

Again, a higher effective rate of interest means that you get to your desired goal faster, or with lower periodical payments.