Question

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 5%. He currently has $110,000 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? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

We need to do retirement planning for a father.

Step-1 Find the amount he need annually after retirement.and That will be have the same purchasing powr as $40000 today.Inflation 5%, period = 10 years.

Value after 10 years be = 40000(1.05)¹⁰

=40000 x 1.62889463

= 65155.7851

He needs $65155.7851 annualy for 25 years starting from day of retirement.

Step - 2 Find the Total investment amount needed after 10 years i.e. after retirement to fulfill his retirement incomes. Calculate the PV of all withdrawals at 7% interest for 25 annual payment.

PV = Annuity + Annuity x cumulative discounting fator@7% for 24 periods

[ For discounting fator you can refer discounting table, or calculate by yourself on excel or calculator. It is sum of (100/107) + (100/107)² ..........+ till (100/107)²⁴]

= 65155.7851 + 65155.7851 x 11.469333

Value after 10 year or at start of retirement = 812449.24

Step 3- Find the FV of your current savings after 10 years. Amount = 110000 @7%

FV = 110000(1.07)¹⁰

= 110000 x 1.96715136

= 216386.65

Step 4- Find the Net amount you needed to accumulate more

= 812449.24 - 216386.65

More amount needed = 596062.59

Step 5 Find annual contribution required

FV = Annuity + Annuity x cumulative annuity factor @7% for 9 years

[ For annuity factor you can refer you annuity table or calculate by yourself. It is sum of (1.07)+(1.07)² +........+ (1.07)⁹]

596062.59 = Annuity + Annuity x 12.816448 [take annuity common]

596062.59 = Annuity (1 + 12.816448)

596062.59 = Annuity x 13.816448

Annuity = 596062.59 / 13.816448

Annuity = 43141.52

Annual contribution required annualy is $43141.52 at the end of every next 10 years.