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 $60,000 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 4%. He currently has $140,000 saved, and he expects to earn 7% annually on his savings. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below.

How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round your intermediate calculations. Round your answer to the nearest cent.

Answer 1

Money does not have the same value in Time o and Time 1. $ 1000 today has more worth and purchasing power than $ 1000 after 10 years. This is mainly due to inflationary effect.Hence to maintain the current expenditure levels in future years, you need to have a higher principal base.

Solution
Input Data	Current Age	50 Years
Input Data	Time to Retire,n1	10 years
Input Data	Expected annual retirement income at present value	60,000
Input Data	Inflation rate	4%
Input Data	Savings interest, r	7%
Input Data	No of years life expected post retirement,n2	25%
Input Data	Current savings	140000
A	Future Value of $ 60,000 at 4% inflation after 10 years	= Present value * (1+Inflation rate)^n1
		=60,000*(1+4%)^10=	88,814.66
	Hence $ 88,814.6571 after 10 years at the time of retirement has the same value of $ 60,000 today
B	Now, the value of the retirement fund is to be calculated using the formula	Annual retirement income * (1-(1+r)^-n2
		r
		=88,814.6571*(1-(1.07)^-25)/.07=	1,035,008.99
	Thus,an amount of $ 1,035,008.99 will give annual retirement income of $ 88,814.66 for the next 25 years
C	Value of current savings $ 140000 after 10 years at 7% interest rate
	Future Value	= Present Value*(1+r)^n
		=140000*(1+7%)^10	275401.19
	Hence at the time of retirement $ 275401.19 will be available to meet the retirement fund out of current savings.
D	Balance savings to be accumulated over the next 10 years to meet the retirement fund	=1035008.99-275401.19	759607.8
E	To pool $ 759607.8 at the end of 10 years, annual savings to me made over the next 10 years at 7% interest rate is calculated as	Amount required
		(1+r)^n0-1
		r
		=759607.8/(((1+7%)^10)-1)/7%
		(((1+7%)^10)-1)/7% =	13.8164
		=759607.8/13.8164	54978.706
	Hence an amount of $ 55,000 per year need to be saved for the next year to meet the retirement fund target