Question

Jack has just retired and has received a lump sum pay-out of $1,300,000. He invests part of this pay-out on an investment property which earns 6 percent per annum and provides a perpetual income to him of $60,000 per year (assuming end-of-year withdrawals). He puts the rest of the pay out in another investment in the form of an annuity which earns 4 percent per annum. He wants to make equal annual withdrawals over the next 10 years from this investment annuity, leaving a balance of zero, to fund some overseas trips and a few other extravagances.

Required

(i) Calculate how much Jack has invested in the investment property.

(ii) Show how much extra Jack can expect to spend each year (assuming end-of-year withdrawals), over and above the $60,000 from the property investment, for the next ten years from the investment annuity. Note: ignore tax in your calculations.

(Accurate to the nearest dollar)

Hi, can someone teach me to concept for this question. For question A, are we supposed to use 60,000/(1- (1+0.03)^10 ? Because after year 10, he would withdraw all his money?

And Part B i have trouble understanding it.

Answer 1

1.

Amount Invested in Investment Property = 60,000/0.06

Amount Invested in Investment Property = $1,000,000

2.

Amount Invested in Annuity = 1,300,000 - 1,000,000 = $300,000

Annuity Interest Rate = 4%

Time Period = 10 years

Calculating Annual Payment,

Using TVM Calculation,

PMT = [PV = 300,000, FV = 0, T = 10, I = 0.04]

PMT = $36,987.28

So,

Annual payment from Annuity = $36,987.28

So, Jack can spend $36,987.28 above $60,000 from investment property.

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We won't use 60,000/(1- (1+0.03)^10 in part A as it is perpetual payment,

Value of Perpetuity = Annual Payment/Interest Rate.