algebra
posted by Blanca on .
Suppose a student wants to be a millionaire in 40 years. If she has an account that pays 8% interest compounded monthly, how much must she deposit each month in order to achieve her goal of having $1,000,000? What is the present value of this annuity?

What is the monthly deposit required to accumulate to a fund of $1,000,000 over a period of 40 years with deposits starting at the end of the first month and bearing an interest rate of 8% compounded monthly?
S(n) = $1,000,000]
i = .08/12 = .00666...
n = 40(12) = 48
R = S(n)(i)/[(1+i)^n  1]
1,000,000(.00666...)/[1.00666...)^481]
$17,746.25
As for the present value,
P = R[1  (1+i)^n]/i
P=17,746.25[1(1.00666...)^40]/.00666...
P = $726,920.