Sinking Funds - SS3 Mathematics Lesson Note

An annuity account set up by the government or a corporation for accumulating funds to meet future debt obligations or purchases is called a sinking fund.

\[R = \frac{S.i}{(1 + i)^{n} - 1}\]

Example 6 \(AJ\ and\ Robertson\ construction\) wants to accumulate \(N100,000\ \)in\(\ 5\ years’\) time to replace worn out equipment. A sinking fund is established by making fixed monthly payments into an account paying \(6\%\) per annum compounded monthly. How much should each payment be?

Solution

\[S = 100000,\ i = \frac{0.06}{12} = 0.005,\ n = 5 \times 12 = 60\]

\[R = \frac{100000 \times 0.005}{(1 + 0.005)^{60} - 1}\]

\[R = \frac{100000(0.005)}{0.337} = 1483.7\]

\[R = N1,483.70\]