Question

You would like to have $1,000,000 in 33 years by making regular deposits at the end of each month in an annuity that pays 7% compounded monthly. Determine the deposit at the end of each month. Do not round until the final answer. Then round to the nearest dollar as needed.

Answer 1

FV of annuity = payment*[(1+r)^n - 1]/r

annual r = 7%
monthly r = (1+7%)^(1/12) - 1 = 0.5654%
n = 33 years = 33*12 = 396

Monthly payment required = 1000000*0.5654%/[(1+0.5654%)^396 - 1]
= 679.1749946
= $679 (rounded)

Answer 2

Future value=
\[
\frac{R
\left((i+1)^n-1\right)}{i}
\]
Where R is the monthly payment
\[
\frac{R
\left((\frac {.07}{12}+1)^{396}-1\right)}{\frac {.07}{12}}=10^6
\]
Solve for R and you get
R=647.64

Answer 3

@smicatrotto r=.07/12

Answer 4

Oh okay, thank you!!