Question

# Your father is 50 years old and will retire in 10 years. He expects to live...

Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as \$40,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 3%. He currently has \$230,000 saved, and he expects to earn 7% annually on his savings. How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Round your answer to the nearest cent.

Year remains in retirement = 10 year

Today purchasing power required after retirement = \$40,000

Interest rate = 7%

Inflation rate = 3%

Real rate of return = (1 + 7%) / (1 + 3%) - 1

= 1.0388 - 1

= 3.88%

Real rate of return is 3.88%.

Income required after 10 year = \$40,000 × (1 + 3%) ^ 9 (All payment at begining of year)

= \$40,000 × 1.304773

= \$52,190.93

First payment required after 10 year will be \$52,190.93.

HE will expected to live 25 year, so total amount required at time of retirement is calculated in excel and screen shot provided below:

Total amount required at time of retirement is \$857,521.41.

Current Saving = \$230,000

Annual saving required to fullfill retirement goal is calculated in excel and screen shot provided below:

Annual Saving required for next 10 year is \$27,400.40.