Excel is a tool for solving problems, but with many time value of money problems

Question

Excel is a tool for solving problems, but with many time value of money problems, you may still need to draw a time line. This is a classic retirement problem. A friend is celebrating her birthday and wants to start saving for her anticipated retirement. She has the following years to retirement and retirement spending goals: Years until retirement: Amount to withdraw each year: Years to withdraw in retirement: Interest rate: 30 $ 90,000 30 8% Because your friend is planning ahead, the first withdrawal will not take place until one year after she retires. She wants to make equal annual deposits into her account for her retirement fund. If she starts making these deposits in one year and makes her last deposit on the day she retires, what amount must she deposit annually to be able to make the desired withdrawals at retirement? Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump sum deposit today to cover her retirement needs. What amount does she have to deposit today? Suppose your friend's employer will contribute to the account each year as part of the company's profit sharing plan. In addition, your friend expects a distribution from a family trust several years from now. What amount must she deposit annually now to be able to make the desired withdrawals at retirement? Employer's annual contribution: Years until trust fund distribution: Amount of trust fund distribution: $ 1,50o $ 25,000

Explanation / Answer

(a) Let the current time be t = 0. Hence, retirement will come at = 30 and retirement withdrawals will start at t=31 and continue uptil t = 60.

Retirement Withdrawals = $ 90000 per annum, Number of Withdrawal Years = 30 and Interest Rate = 8 %

Present Value of Retirement Withdrawals at t = 30 will be:

PV(30) = 90000 x (1/0.08) x [1-{1/(1.08)^(30)}] = $ 1013201

Let her annual equal deposits into the retirement fund be $ K per annum

Therefore, the Future Value of these deposits at t=30 should be equal to PV(30).

K x (1.08)^(29) + K x (1.08)^(28) + .............+ K = 1013201

K = $ 8943.96 or $ 8944 approximately.

Let the lumpsum deposit be $ M which when compounded for 30 years at 8 % per annum should be equal to PV(30).

M x (1.08)^(30) = 1013201

M = $ 100689.16

Let the annual deposits by the friend alone be $ N and this combined with the employer's annual contribution of $ 1500, makes annual contribution equal to $ (1500 + N). The future value of these annual contributions plus the future value of the trust fund distribution of $ 25000 should be equal to PV(30).

(1500 + K)^(29) + (1500 + K)^(28) + ..........+ (1500 + K) + 25000 x (1.08)^(30-20) = 1013201

N = $ 6967.516 ~ $ 6967.52

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