if you invest at the end of every month, use FVordinary annuity...
FVoa = PMT [((1 + i)^n - 1) / i]
n = 12 * 12 = 144
i = 0.11 / 12 = 0.00917
= 50[(1.00917^144) - 1) / 0.00917]
= 50[2.72098 / 0.00917]
= 50[296.83406]
= $14,841.70
If payment are made at the beginning of each month, use FV annuity due "FVad", which is simply:
FVoa(1 + i)
= 14,841.70(1.00917)
= $14,977.75
What would be your future account value (after-tax and after-inflation) if you invested $125 each month into a growth mutual fund for 20 years? Assume an average annual rate of return of 12.5 percent. Assume a combined federal and state income tax of 24% and an average inflation rate of 3.8% over the 20-year period.
after tax rate: 0.125 * (1 - tax) = 0.125*0.76 = 0.095
( 1 + Real rate) = (1 + Nominal rate) / (1 + inflation rate)
1 + real = 1.095 / 1.038
1 + real = 1.05491
real = 0.05491
i = 0.05491 /12 = 0.00458
n = 12 * 20 = 240
FVoa = 125[(1.00458^240) - 1) / 0.00458]
= 125[435.18583]
= $54,398.23
if payments are made at the beginning of each month...use FVad
FVad = FVoa (1 + i)
= 54,398.23(1.00458)
= $54,647.16
My calculator kept all the numbers in its memory and I did not round until the end, so my answers may be off slightly vs. rounding the rates as you go....e.g. the 0.05491 real rate is actually 0.05491330 in my calculator, so if you'd rounded to say 0.0549 your answer would be less. My "i" in the equation was 0.00457611 with no rounding. Try re-working the problem with the lower, rounded number.
An investment of $50 per month in a fund earning 11% per year will grow to $14,978 after 12 years. Here is an online calculator to solve the problem:
http://googolplex.cuna.org/13590/ajsmall...
Go to bankrate.com. You will find calculators for everything. I did get your answer there but if this is a school project it is better that you go in and research it yourself.
FV of an annuity
Were you to invest $50 each month into a mutual fund which averaged an 11% annual return, what would be the mutual fund account value after 12 years? Ignore the impact of taxes and inflation.
Answer
$14,977.75
$14,841.70
$15,126.98
$13,627.91
What would be your future account value (after-tax and after-inflation) if you invested $125 each month into a growth mutual fund for 20 years? Assume an average annual rate of return of 12.5 percent. Assume a combined federal and state income tax of 24% and an average inflation rate of 3.8% over the 20-year period.
Answer
$133,689.95
$54,389.77
$132,311.70
$54,638.60
