Question

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 %5,100 at the end of each year into a Roth IRA for the next 40 years. If you earn 10 percent compounded annually on your investment, how much will you have when you retire in 40 years? How much will you have if you wait 10 years before beginning to save and only make 30 payments into your retirement account?

Answer 1

Investment of $5100 at the end of each year for next 40 years.

return rate = 10%

So using formula FV = A*((1+r)^n - 1)/r

where A = 5100

r = 10%

n = 40 years

So, FV = 5100*((1.1^40 - 1)/0.1 = $2257222.03

Amount in account at the time of retirement = $2257222.03

If no payment are made for initial 10 years and after that,30 payment each of $5100 is made. So now,

A = 5100

r = 10%

t = 30 years

So FV at retirement = 5100*((1.1^30 - 1)/0.1 = $838919.52