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What annual amount is required to deposit for five years to accumulate the amount of money with the same purchasing power as \$ 680.58 today if the interest rate at market value is 10% per year and inflation is 8% per year?

Solution First, find the actual number of future (inflated) dollars that will be required five years from now equivalent to \$ 680.58 today. This is case 3 and Eq. (14.10) applies. F = (current purchasing power) (1 + ƒ) 5 = 680.58 (1.08) 5 = \$ 1,000 The actual amount of the annual deposit is calculated with the interest rate (inflated) at market value of 10%. This is case 4 where A is calculated for a given F value. A = 1,000 (A / F, 10%, 5) = \$ 163.80

Comment The real interest rate is i = 1.85%, as determined by equation (14.9). To put the above calculations in perspective, if the inflation rate is zero when the real interest rate is 1.85%, the amount of future money with the same purchasing power as \$ 680.58 today is, in effect, \$ 680.58. So the annual amount required to accumulate this future amount in five years is A = 680.58 (A / F, 1.85%, 5) = \$ 131.17. That is, \$ 32.63 less than the \$ 163.80 calculated before, where ƒ = 8%. This difference is due to the fact that, during inflationary periods, the dollars deposited have more purchasing power than the dollars recovered at the end of the period.     