Question

You are assisting your client, Selena Hermione with her retirement planning Selena would like to have retirement income of 85% of her current salary of $120,000 Selena is currently 30 years from retirement and is planning for 20 years in retirement She currently has a retirement fund of $250,000 You are allowing fo inflation of 2.5% annually and expect to earn an 8% after-tax return Please work through the questions below determine how much Selena should save annually toward retirement.

a. Adjusting for inflation, how much income will Selena need to provide for her first year of retirement?

b. How much capital will she need at retirement to fund those living expenses? She plans to take annual withdrawals at the BEGINNING of each year. Please allow for an annual cost of living increase.

c. How much should Selena invest at the END of each year to provide her with that amount of capital retirement, considering that she currently has $250,000 saved for retirement?

Answer 1

a]

Retirement income required in 1st year of retirement (in today's dollars) = current income * 85% = $120,000 * 85% = $102,000

This needs to be increased by inflation rate of 2.5% for 30 years

Retirement income required in 1st year of retirement = $102,000 * (1 + 2.5%)³⁰ = $213,951.89

b]

This is calculated using the formula for present value of growing annuity, with growth rate being the inflation rate

PV = [P * (1 + r) / (r - g)] * [1 - ((1 + g) / (1 + r))ⁿ] , where

P = first payment, which is $213,951.89

r = rate of return, which is 8%, or 0.08

g = inflation rate, which is 2.5%, or 0.025

n = number of years, which is 20

PV = [$213,951.89 * (1 + 0.08) / (0.08 - 0.025)] * [1 - ((1 + 0.025) / (1 + 0.08))²⁰]

PV = $2,724,240.91

c]

Future value of annuity = P * [(1 + r)ⁿ -1] / r,

where P = amount deposited each year

$2,724,240.91 = P * [(1 + 0.08)³⁰ - 1] / 0.08

P = $24,048.06