# algebra

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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?

• algebra -

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...)^48-1]
\$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.

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