Suppose you wish to retire 35 years from today. You determined that you will nee

Question

Suppose you wish to retire 35 years from today. You determined that you will need $250,000 per year after you retire, with the first retirement funds withdrawn one year from the day you retire and that you will need to make 28 such withdrawals. Assuming that you can earn 5% per year on your retirement funds. PLEASE SHOW THESE ANSWERS IN EXCEL

a) How much must you deposit in an account today (lump sum), so that you may have enough funds for retirement?

b) If you cannot afford to make a single lump sum deposit, today, to support your retirement. How much must you deposit at the end of each year for the next 35 years so that you have enough funds for your desire retirement? Assuming the last deposit will be made on the day you retire.

Explanation / Answer

Soln : a) Step1 : Let X be the amount that needs to be deposited today to get the amount of 250000 per year for 28 years after retirement.

Step 2 : We need to calculate the Lump sum amount first needed at the ime of retirement.

So, it is constant series of amount 250000 , Time value of money to be used with discount rate as 5%

Amount , A = 250000*(P/A,5%, 28) *(F/P, 5%, 1) = 250000*((1.05)28-1)/(0.05*1.0528) * (1.05) = 3910758 (approx)

P/A. 5%, 28 will get the amount of series one year earlier than the first year of payment , So using (F/P, 5%,1) to get it at the end of retirement.

Now this amount needs to be converted into current value , V = 3910758*(P/F,5%,35) = 3910758/(1.05)35 = 708982 (approx.)

b) Now, he can not deposit this amount together in one go, so he put Y amount on yearly basis for 35 years.

We have to spread this V amount in next 35 years, Y = V*(A/P,5%, 35) = 708982*((0.05*(1.05)35/((1.05)35 -1 ) = 43299 (approx.) is the amount to be kept each year for getting the retirement funds.

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