Today is your 40th birthday. You expect to retire at age 65, and actuarial tables suggest that you will live to be 100. You want to move to Hawaii when you retire. You estimate that it will cost you exist200,000 to make the move (on your 65th birthday), and that your annual living expenses will be exist25,000 a year after that. You expect to cam an annual return of 7% on your savings. (a) How much will you need to have saved by your retirement date? (b) You already have exist50,000 in savings. How much would you need to save at the end of each of the next twenty-five years to be able to afford this retirement plan? (c) If you did not have any current savings and did not expect to be able to start saving money for the next five years (that is, your first savings payment will be made on your 45th birthday). how much would you have to set aside each year alter that to be able to afford this retirement plan?

(a) How much will you need to have saved by your retirement date?

first of all, we need to determine how much money you will need to have when you are 65 years old:

total = $523,700

(b) You already have $50,000 in savings. How much would you need to save at the end of each of the next twenty-five years to be able to afford this retirement plan?

we have to calculate the FV of $50,000 = $50,000 x (1 + 7%)²⁵ = $271,372

so you need $523,700 - $271,372 = $252,328 by the time you are 65

we will now use the future value of an ordinary annuity formula:

FV = payment x annuity factor

$252,328 = payment x 63.249 (FV annuity factor, 7%, 25 years)

payment = $252,328 / 63.249 = $3,989.44

(c) If you did not have any current savings and did not expect to be able to start saving money for the next five years (that is, your first savings payment will be made on your 45th birthday). how much would you have to set aside each year alter that to be able to afford this retirement plan?

FV = payment x annuity factor

$523,700 = payment x 40.995 (FV annuity factor, 7%, 20 years)

payment = $523,700 / 40.995 = $12,774.73

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