Question

He is contemplating some long term investments he could undertake to secure his future and that if his children. He is now 50 years old and he plans to retire in 10 years from active farm work. He expects to live for another 25 years after he retires –that is, until age 85. He was advised by a friend that an investment in the financial market will help him plan his retirement well. He has no idea about financial markets and how they operate. You recently graduated and have just reported to work as an investment advisor at the brokerage firm of Cenden Ltd. King Solomon has approached your company for advice. Your boss after a discussion with King Solomon could gather the following information. King Solomon wants his first retirement payment to have the same purchasing power at the time he retires as GHȼ 40,000 has today. He wants all of his subsequent retirement payments to be equal to his first retirement payment. (Do not let the retirement payments grow with inflation: King Solomon realizes that the real value of his retirement income will decline year by year after he retires.) His retirement income will begin the day he retires, 10 years from today, and he will then receive 24 additional annual payments. Inflation is expected to be 5% per year from today forward. He currently has GHȼ 100,000 saved up, and he expects to earn a return on his savings of 8% per year with annual compounding.

a. To the nearest cedi, how much must he save during each of the next 10 years (with equal deposits being made at the end of each year, beginning a year from today) to meet his retirement goal? (Note: Neither the amount he saves nor the amount he withdraws upon
retirement is a growing annuity.)                                                   

Answer 1

Annual retirement income needed= Current value*(1+i)^n

Where i- inflation rate and n= Period in between (number of years)

Given,

Current value= GHȼ 40,000.   Inflation expected= 5% per year. Time to retire= 10 years

Substituting these values, annual retirement income= 40,000*(1+5%)^10= GHȼ 65,155.79

Amount required as on the date of retirement (PV of annuity due comprising retirement income for 25 years= GHȼ 751,165.30 as follows:

Future value of current savings, as on the date of retirement= GHȼ 100,000*(1+8%)^10

= GHȼ 215,892.50

Net amount to be accumulated by the retirement date= 751,165.30 - 215,892.50 = 535,272.80

Amount to be saved annually, at the end of each year, over the next 10 years= GHȼ 36,950 as follows