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(Related to The Business of Life: Saving for Retirement) (Future value of an ord

ID: 2809424 • Letter: #

Question

(Related to The Business of Life: Saving for Retirement) (Future value of an ordinary annuity) You are graduating from college at the end of this semester and after reading the The Business of Life box in this chapter, you have decided to invest $5,300 at the end of each year into a Roth IRA for the next 43 years. If you earn 9 percent compounded annually on your investment, how much will you have when you retire in 43 years? How much will you have if you wait 10 years before beginning to save and only make 33 payments into your retirement account? How much will you have when you retire in 43 years? $(Round to the nearest cent.)

Explanation / Answer

a.Future value of annuity=Annuity[(1+rate)^time period-1]/rate

=$5300[(1.09)^43-1]/0.09

=$5300*440.8456649

=$2,336,482.02(Approx)

b.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

Hence

A=$5300*(1.09)^32+$5300*(1.09)^31+$5300*(1.09)^30+.................+$5300*(1.09)^1+$5300

=$5300*[(1.09)^32+(1.09)^31+(1.09)^30+...............+(1.09)^1+1]

=$5300*179.8003153

=$952941.67(Approx).