Question

Bonnie has decided to begin a retirement savings program where she will contribute to an account that will accumulate tax free throughout her working life. She expects to retire in exactly 9 years from today, and her goal is to have accumulated the amount of $600000 when she reaches her future retirement age. In order to meet her goal, she will begin making MONTHLY contributions to a special account devoted to the retirement goal. Contributions to this account will begin one month from today, and she will continue placing equal monthly amounts into her retirement account for the next 9 years. What minimum amount needs to be placed in her account at the end of each month so that she'll reach her goal if the annual interest rate is 9%.

Answer 1

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
FV of Annuity	$   6,00,000.00
Int Rate	0.7500%
Periods	108

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
$600000 = Cash Flow * [ [ ( 1 + 0.0075 ) ^ 108 ] - 1 ] / 0.0075
$600000 = Cash Flow * [ [ ( 1.0075 ) ^ 108 ] - 1 ] / 0.0075
$600000 = Cash Flow * [ [ ( 2.2411 ] - 1 ] / 0.0075
$600000 = Cash Flow * [ 1.2411 ] / 0.0075
Cash Flow = $ 600000 * 0.0075 / 1.2411
Cash Flow = $ 3625.75

Her monthly deposit shall be $ 3625.75