3.3.4 Equal-Payment Series Sinking Fund In this type of investment mode, the objective is to find the equivalent amount (A) that should be deposited at the end of every interest period for n interest periods to realize a future sum (F) at the end of the nth interest period at an interest rate of i. The corresponding cash flow diagram is shown in Fig. 3.6. F 0 1 2 3 4 A A A A A i % Fig. 3.6 Cash flow diagram of equal-payment series sinking fund. 32 Engineering Economics In Fig. 3.6, A = equal amount to be deposited at the end of each interest period n = No. of interest periods i = rate of interest F = single future amount at the end of the nth period The formula to get F is i A = F = F(A/F, i, n) (1 + i)" - 1 where (A/F, i, n) is called as equal-payment series sinking fund factor. EXAMPLE 3.4 A company has to replace a present facility after 15 years at an outlay of Rs. 5,00,000. It plans to deposit an equal amount at the end of every year for the next 15 years at an interest rate of 18% compounded annually. Find the equivalent amount that must be deposited at the end of every year for the next 15 years