Posted by **beech** on Tuesday, October 11, 2011 at 9:58am.

3. 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 -
**Steve**, Tuesday, October 11, 2011 at 10:52am
P(1+.08/12)^40 = 1000000

P*21.72 = 1000000

P = $46040.52

- algebra -
**Steve**, Tuesday, October 11, 2011 at 10:57am
Oops. Monthly deposits.

Let r = 1 + .08/12 = 1.00666666

M (r^480 - 1)/(r-1) = 1000000

3641.007M = 1000000

M = $274.65

Anyone see an error here?

- algebra -
**Reiny**, Tuesday, October 11, 2011 at 11:44am
Steve, your method is correct,

I let my calculator carry its maximum digits and got

$286.45

Also the present value of $1000000 40 years from now at 8% compounded monthly

PV (1.00666666..)^480 = 1000000

PV = $41197.40

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