Answer:
a. How much will you have in your retirement account on the day you retire?
we must calculate the future value of an annuity:
future value = annuity payment x {[(1 + r)ⁿ - 1] / r} = $6,500 x {[(1 + 0.065)⁴² - 1] / 0.065} = $1,308,262.21
b. If, instead of investing $ 6,500 per year, you wanted to make one lump-sum investment today for your retirement that will result in the same retirement saving, how much would that lump sum need to be?
future value of lump sum = lump sum x (1 + r)ⁿ
$1,308,262.21 = lump sum x (1 + 0.065)⁴²
lump sum = $1,308,262.21 / (1 + 0.065)⁴² = $1,308,262.21 / 14.08262214 = $92,899.05
c. If you hope to live for 26 years in retirement, how much can you withdraw every year in retirement (starting one year after retirement) so that you will just exhaust your savings with the 26th withdrawal (assume your savings will continue to earn 11.0% in retirement)?
present value of an annuity = annuity payment x {[1 - 1/(1 + r)ⁿ
] / r}
annuity payment = $1,308,262.21 / {[1 - 1/(1 + r)ⁿ
] / r} = $1,308,262.21 / {[1 - 1/(1 + 0.11)²⁶
] / 0.11} = $1,308,262.21 / 8.48806 = $154,129.74
