You are graduating from college at the end of this semester and you have decided

Question

You are graduating from college at the end of this semester and you have decided to invest $4,900 at the end of each year into a Roth IRA for the next 48 years. If you earn 6 percent compounded annually on your investment, how much will you have when you retire in 48 years? How much will you have if you wait 10 years before beginning to save and only make 38 payments into your retirement account?

How much will you have when you retire in 48 years?

How much will you have if you wait 10 years before beginning to save and only make 38 payments into your retirement account?

Explanation / Answer

Future value of annuity = P×[(1+r)^n-1]÷r

P is Principal payable

r is interest rate

n is number of payments

= $4,900×[(1+6%)^48-1]÷6%

= $1,257,166

Waiting 10 years before deposit:

= $4,900×[(1+6%)^38-1]÷6%

= $665,931

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