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?

Answer 1

P(1+.08/12)^40 = 1000000
P*21.72 = 1000000
P = $46040.52

Answer 2

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?

Answer 3

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