Answer:
(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:
- $200,000 to move to Hawaii
- distributions for 35 years (annuity) = $25,000 x 12.948 (PV annuity factor 7%, 35 years) = $323,700
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
