You plan to retire in exactly 20 years. Your goal is to create a fund that will

Question

You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $20,000 at the end of each year for the 30 years between retirement and death (a psychic told you that you’d die exactly 30 years after you retire). You know that you will be able to earn 11% per year during the 30-year retirement period. Required:

a. How large a fund will you need when you retire in 20 years to provide the 30-year, $20,000 retirement annuity?

b. How much will you need today as a single amount to provide the fund calculated in part (a) if you earn only 9% per year during the 20 years preceding retirement?

c. What effect would an increase in the rate you earn both during and prior to retirement have on the values found in parts (a) and (b)? Explain.

d. Now assume that you will earn 10% from now through the end of your retirement. You want to make 20 end-of-year deposits into your retirement account that will fund the 30-year stream of $20,000 annual annuity payments. How large do your annual deposits have to be?

Explanation / Answer

A) AMOUNT OF MONEY THAT WILL BE BE NEEDED AT THE AGE OF RETIREMENT AFTER 20 YEARS WILL BE THE PRESENT VALUE OF ANNUITY DISCOUNTED AT THE RATE OF 11%.

This can be done in excel by using PV function and putting r=11% nper=30 PMT=$20000 FV=0 and we get PV as $1,73,875.85. This is the amount of fund needed at the age of retirement which will grow at 11% and provide an annuity of $20,000 for 30 years

B) AMOUNT NEEDED TODAY IF WE CAN EARN 9% TODAY WILL BE PRESENT VALUE OF $1,73,875.85 THAT WE WILL HAVE AFTER 20 YEARS WILL BE SIMPLY THE DISCOUNTED VALUE OF THIS AMOUNT

= $1,73,875.85 /(1.09^20) = $31024.82289

C) INCREASE IN THE RATE WILL LEAD TO DECLINE IN THE VALUE OF A LARGE FUND ON THE DATE OF RETIREMENT AND HENCE LOWER DISCOUNTED VALUE AS ON TODAY. LESSER AMOUNT OF LARGER FUND WILL BE NEEDED BECAUSE WE ARE EARNING HIGHER RATE OF INTEREST ON THE FUNDS INVESTED AND HENCE TO GET SAME AMOUNT OF $20000 DOLLAR LESSER AMOUNT NEEDED TO BE INVESTED AS RATE HAVE INCREASED AND HENCE LOWER PRESENT VALUE.

CHANGING THE VALUE TO 12% WILL RESULT IN VALUE OF LARGER FUND $161103.68 AND PRESENT VALUE IS $28745.8728

D) NOW WE HAVE TO FIND VALUE OF ANNUITY THAT IS PMT IN THIS CASE. WE ARE GIVEN FV AFTER 20 YEARS WHICH IS THE AMOUNT WE HAVE COMPUTED IN PART (A)

WE WILL USE PMT FUNCTION IN EXCEL SAME CAN BE DONE IN FINANCIAL CALCULATOR

PUTTING NPER=20 FV= $1,73,875.85 INT RATE=10% PV=0 WE WILL GET PMT AS $3035.81

THIS IS THE AMOUNT OF ANNUITY THAT WILL BE DEPOSITED IN EACH OF END OF 20 YEARS AND WILL GROW TO $173875.85 THAT WILL BE SUFFICIENT TO PROVIDE 30 YEAR STREAM OF $20,000.

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