Question

How much do you need to invest in equal annual amounts for the next 10 years (year 1 thru 10) if you want to withdraw $5,000 at the end of the eleventh year and increase the annual withdrawal by $1,000 each year thereafter until year 25 (your last withdrawal is year 25)? The interest rate is 12%, compounded monthly.

Answer 1

Let us assume you will be depositing an amount equal to $ A.

Interest rate = 12% compounded monthly

First of all convert it to effective rate of interest.

jejs = [1 + inom ju – 1 m

$\large \implies i_{eff} = [1 + \frac{0.12}{12}]^{12} -1$

left = 0.1268

Interest rate = 12.68% per year

The Future value of investment can be determined as

F = A(F/A,12.68%,10)

=> F = A(1.1268¹⁰ - 1)/0.1268

=> F = 18.13827A

You will be withdrawing $ 5000 every year starting from 11th year and last deposit will be end of year 25. Each withdrawal will be $ 1,000 greater than previous.

Calculate the present value of the withdrawal

P = 5,000(P/A, 12.68%, 15) +1,000(P/G, 12.68%,15)

S P 1-1.1268-15 = 5,000 x = 1.126815 – 0.1268 x 15 - 1 0.12682 x 1.126815 0.1268 +1,000x=

S P =5,000 X 6.5698 +1.000 x 32.0761

S P = 32.849.06 + 32,076.17

S P = 64,925.23

The present value of the withdrawal at the end of year 10 is equal to $ 64,925.23. now equate future value and present value

18.13827A = 64,925.23

= A =- 64,925.23 18.13827

A = $ 3,579.46

You are required to deposit $ 3,579.46 every year.

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