Question

You annually (at the end of the year) invest $1,500 in an individual retire-

ment account (IRA) starting at the age of 20 and make the contributions for 10 years,

(until the age of 30), after which you make no more contributions and just let the money

grow at the account’s annual interest rate. Your twin sister annually (at the end of the

year) invests $1,500 in an individual retirement account starting at age 30 and makes

the contributions for 30 years (until she turns 60). Both of you earn 7 percent annually

on your investment. (MUST BE DONE ON EXCEL)

(a) How much do you have in your account when you are 60 years old?

(b) How much does your sister have in her account when she is 60 years

old?

(c) Comparing your answers from parts (a) and (b), what is an implication

of the result?

Answer 1

A) 1500 invested every year for 10 yrs and amount sits in account for 30 yrs, i = 7%

We use FV(rate, time, per year payment, present value) function in excel

Yearly investment			$1,500.00
Total investment years			10
interest			7%
Amount sits in account undisturbed (yrs)			30
Future value at the end of investment (10 yrs)			$20,724.67
Future value after 30 more years			$1,57,761.49

Showing formula in excel

Yearly investment		1500
Total investment years		10
interest		0.07
Amount sits in account undisturbed (yrs)		30
Future value at the end of investment (10 yrs)		=FV(E18, E17,-E16)
Future value after 30 more years		=FV(E18,E19,0,-E20)

B) 1500 invested every year for 30 yrs, i = 7%

Yearly investment		$1,500.00
Total investment years		30
interest		7%
Future value at the end of investment (30 yrs)		$1,41,691.18

Showing formula in excel

Yearly investment		1500
Total investment years		30
interest		0.07
Future value at the end of investment (30 yrs)		=FV(E25, E24,-E23)

C) person has more amount in your IRA account than his sister because he started saving early and initial amount got compounded for more no of year.