Question

You will deposit $10,000 today. It will grow for 8 years at 10% interest compounded semiannually. You will then withdraw the funds annually over the next 6 years. The annual interest rate is 8%. Your annual withdrawal will be: Use Appendix A and Appendix D to calculate the answer.

Answer 1

- Amount Invested today = $10,000

Interest rate = 10% interest compounded semiannually

calculating effective Annual Rate(EAR);-

Where,

r = Interest rate = 10%

m = no of times compounding in a year = 2 (compounded semi-annually)

EAR = 10.25%

- Calculating Future Value at the end of 8 years:-

Future Value = Invested Amount*(1+EAR)^{n}

Where,

EAR = 10.25%

n= no of periods = 8 years

Future Value = $10,000*(1+0.1025)^8

= $10,000*2.18287458838

Future Value = $21,828.75

Now, from this value you will withdraw annually for 6 years.

Calculating Annual Withdrawal amount using PV of annuity formula:-

Where, C= Periodic Withdrawal

r = Periodic Interest rate = EAR = 10.25%

n= no of periods = 6 years

C = $5048.82

So, Your annual withdrawal will be is $5048.82

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