45, wants to retire at age 60. He currently earns $60,000 per year. His goal 80%

Question

45, wants to retire at age 60. He currently earns $60,000 per year. His goal 80% of his preretirement income. He wants the retirement in inflation. Bill has an investment portfolio valued at $150,000, which come to be djusted for is cur ing 10% average annual returns. Bill expects inflation to avera Bill is currently ge 3% and, based on his family health, predicts he will live to age 90. of his gross income at each year-end and expects continue wants to ignore any Social Security benefits for ts to continue this level of aving 7% 1. What will Bill's annual income needs be at age 60? 2. Will the need be for an ordinary annuity or an annuity due? 3. How much total capital will Bill need at age 60? 4. How much capital will Bill have at age 60? 5. Will Bill have enough income at retirement? 6. What is the earliest age that Bill could retire utilizing the current savings and this level of savings. Bill to ignore any Social Security benefits for purposes of retirement planning 7. How much would Bill need to increase his savings on an annual basis to me 8. Even assuming that Bill increases his savings to an appropriate amount, wh 9. How could the capital needs analysis be modified to reduce the risks iden investment plan? goal of retiring at age 60? the risks that may affect the success of the plan? above?

Explanation / Answer

1) Bill's retirement income needs at age 60 = Current Salary x 80% x (1 + inflation)^15

= 60,000 x 80% x (1 + 3%)^15

= $74,782.44

2) He would need an annuity due that pays at the beginning of the year to meet his retirement needs.

3) Using present value for growing annuity formula,

PV = P / (r - g) x [1 - ((1 + g) / (1 + r))^n]

Here, P = 74,782.44, r = 10%, g = 3%, n = 30

=> PV = $919,714..08 is the amount he needs.

4) Bill currently invest 7% x 60,000 = 4,200 each year, which will grow at the rate of inflation. Using future value of growing annuity formula and future value of his investment portfolio,

FV = P / (r - g) x [(1 + r)^n - (1 + g)^n] + PV x (1 + r)^n

Here, P = 4,200, r = 10%, g = 3%, n = 15, PV = 150,000

=> FV = $783,744.08 is the amount he will have at retirement.

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