Question

How much should you invest each month in order to have $800,000 if your rate of return is 8% compounded monthly and you want to achieve your goal in 40 years? $

How much interest will you earn? $

How much should you invest each month in order to have $800,000 if you want to achieve your goal in 20 years? $

If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?

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
FV of Annuity = CF [ (1+r)^n - 1 ] / r

If Annuity is for 40 Years:

800000 = CF [ ( 1 + 0.006667)^480 - 1 ] / 0.006667

= CF [ ( 1.006667)^480 - 1 ] / 0.006667

= CF [ 24.2734 - 1 ] / 0.006667

= CF [ 23.2734 ] / 0.006667

CF = 800000 * 0.006667 / 23.2734

= $ 229.16

If Annuity is for 20 Years:

800000 = CF [ ( 1 + 0.006667)^240 - 1 ] / 0.006667

= CF [ ( 1.006667)^240 - 1 ] / 0.006667

= CF [ 4.9268 - 1 ] / 0.006667

= CF [ 3.9268 ] / 0.006667

CF = 800000 * 0.006667 / 3.9268

= $ 1358.19

If Annuity is for 10 Years:

800000 = CF [ ( 1 + 0.006667)^120 - 1 ] / 0.006667

= CF [ ( 1.006667)^120 - 1 ] / 0.006667

= CF [ 2.2196 - 1 ] / 0.006667

= CF [ 1.2196 ] / 0.006667

CF = 800000 * 0.006667 / 1.2196

= $ 4372.87

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