Question

If you set aside $5,000 per year (i.e., one deposit of $5,000 each year) in a Roth IRA for the next 25 years (the first
contribution is to be made exactly one year from now, so use an ordinary annuity setup), how much will you have at
your retirement in 25 years if your IRA earns 6% APR, compounded monthly?

Answer 1

Effective Annual Rate:

Particulars	Amount
Ret period	0.5000%
No. of periods	12.0000

EAR = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.005 ) ^ 12 ] - 1
= [ ( 1.005 ) ^ 12 ] - 1
= [ 1.0617 ] - 1
= 0.0617
I.e EAR is 6.17 %

FV of Annuity :
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$      5,000.00
Int Rate	6.168%
Periods	25

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 5000 * [ [ ( 1 + 0.06168 ) ^ 25 ] - 1 ] / 0.06168
= $ 5000 * [ [ ( 1.061678 ) ^ 25 ] - 1 ] / 0.061678
= $ 5000 * [ [4.465] - 1 ] / 0.061678
= $ 5000 * [3.465] /0.061678
= $ 280893.48

Amount in Account after 25 years is $ 280893.48