Question

An individual wants to have $95,000 per year to live on when she retires in 30 years. The individual is planning on living for 20 years after retirement. If the investor can earn 6% during her retirement years and 10% during her working years, how much should she be saving during her working life? (Hint: Treat all calculations as annuities.)

Answer 1

annual contribution = $6,624.25

total amount saved in 30 years = $1,089,650

Step-by-step explanation:

time until retiring = 30 years

interest rate earned until retiring = 10%

she plans to live 20 years after retiring

interest rate earned after retiring = 6%

expected distribution = $95,000 per year

in order for her to be able to have the 20 payments of $95,000, she will need:

= annual payment x PV annuity factor

• annual payment = $95,000
• PV annuity factor (6%, 20 periods) = 11.470

total amount needed = $95,000 x 11.47 = $1,089,650

in order to determine the annual contribution we need to use the future value of an annuity formula:

FV = annual payment x FV annuity factor

• FV = $1,089,650
• FV annuity factor (10%, 30 periods) = 164.494

annual payment = $1,089,650 / 164.494 = $6,624.25