You want to be able to withdraw $800 from a savings account at the end of year 1

Question

You want to be able to withdraw $800 from a savings account at the end of year 1, $900 at the end of year 2, 1,000 at the end of year 3, and so on over a total of 5 years. How much must must be deposit right now, at the end of year o, to just deplete the account after the 5 withdraws if the interest is 5% compounded annually?

Explanation / Answer

We know that F = p (1 + i)^n F= fututre value, p = present value, i = interest rate = 5 %, n = time period Let us consider year 5: 1200 = p5(1+ 0.05) => p5= 1200/1.05 = 1142.86 year 4: (1142.86+1100) = p4 (1 + 0.05) => p4 = 2242.86/1.05 = 2136.06 year 3: (2136.06 + 1000) = p3(1 + 0.05) => p3 = 3136.06/1.05 = 2986.72 year 2: (2986.72 + 900) = p2(1 + 0.05) => p2 = 3886.72/1.05 = 3701.64 year 1: (3701.6 + 800) = p1(1 + 0.05) => p1 = 4501.6/1.05 = 4287.24 = our answer

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