Question

Two friends, Kyle and Wes, graduated college and started working on their career at the same time. Both friends were 25 at the time.

As soon as Kyle was eligible for the 401K benefit he started depositing $100 per month for the next ten years.

Wes decided he so enjoyed having a real income that he wanted to spend it on fast cars, awesome threads, the most recent smart phone and video game system, and clubbing every weekend. Wes chose not to invest in his 401K for a while.

After ten years, Kyle decided to buy a house and couldn't afford to invest in his 401K anymore, so he stopped with his $100 per month deposit, but never touched his balance.

After ten years, Wes's party days were slowing down, he no longer needed the fancy clothes, and didn't need the newest gadgets as much, so he started investing $100 per month in his 401K for the next twenty years.

Both friends averaged 8% over the life of their investment in a mixed mutual fund.

At age 55, the friends decided to see where they stood for retirement savings. Calculate the following:

1. What is Wes' total investment after investing $100 per month for 20 years?

2. Who has the higher balance?

3. What does this tell us about the time value of money?

Answer 1

Rate is assumed to be compounded monthly
Calculation of kyle's money after at the age of 55years
	Future value of annuity($100 per month deposited for 10 years)			=	P[{(1+r)^n}-1]/r
		where
			P	=	$100
			r	=	8%/12 =0.6667% or 0.006667
			n	=	10 years*12 months=120 months
	Money after 10 years			=	100*[{(1+0.006667)^120}-1]/0.006667
				=	100*[2.2196-1]/0.006667
				=	100*1.2196/0.006667
				=	$     18,293.09
	Future value (after 20 more years i.e 30 years from today)			=	Amount*(1+r)^n
		where
			amount	=	$     18,293.09
			n	=	20 years*12 months =240
			r	=	8%/12 =0.6667% or 0.006667
	Future value			=	18293.09*(1+0.006667)^240
				=	18293.09*4.9272
				=	$     90,133.71
	Total amount at the age of 55 for kyle			=	$     90,133.71
1)	calculation of Wes's total investment
	Future value of annuity (after 20 more years i.e 30 years from today)			=	P[{(1+r)^n}-1]/r
			amount	=	$100
			n	=	8%/12 =0.6667% or 0.006667
			r	=	20 years*12 months=240
	Future value of annuity			=	100*[{(1+0.006667)^240}-1]/0.006667
				=	100*[4.9268-1]/0.006667
				=	100*3.9268/0.006667
					$     58,899.06
	Total amount at the age of Wes			=	$     58,899.06
2)	Kyle has higher balance at the age of 55.
3)	It tells us about time value of money that the early you start saving (or investing),the more it is beneficial in the long term.
	It is better to save a dollar today then 10 tommorrow
	Note-there may be slight difference in answer due to decimal points.
	Also the rate is assumed to be compounded monthly.This is the reason 8% has been divided by 12 to get monthly rate of 8%/12 =0.6667% or 0.006667
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	In case you have any doubt,pleaseask in the comments