Question

(a). A college student is 23 years old and a recent graduate. He wants to start saving for his retirement. He plans to save $2000 per year in
an online stock account that pays annual return of 12%. If he sticks to the plan, how much money will he have at the age of 65? (make a
time-line).
(b). Suppose he starts saving for the retirement at the age of 40. If he uses the same plan above, how much money will he have at the age
of 65?
(c). What advice regarding savings will you give to the college graduate? (Analyze and interpret the findings above).

Answer 1

FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / i)
	Investment started at 23	Investment started at 40
Where:
P = the future value of an annuity stream	A	A
PMT = the dollar amount of each annuity payment	$                              2,000	$                              2,000
r = the effective interest rate (also known as the discount rate)	12%	12%
n = the number of periods in which payments will be made (65-23), (65-40)	42	25
FV of annuity at age 65=	PMT x ((((1 + r) ^ n) - 1) / r)	PMT x ((((1 + r) ^ n) - 1) / r)
FV of annuity at age 65=	2000*((((1 + 12%) ^ 42) - 1) / 12%)	2000*((((1 + 12%) ^ 25) - 1) / 12%)
FV of annuity at age 65=	$                       1,928,719	$                          266,668
As we can see that the investment started early has yielded such a massive difference in the retirement corpus and hence we can say that he should start as early as possible
to have a hefty retirement corpus.