Posted by beech on .
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,
P(1+.08/12)^40 = 1000000
P*21.72 = 1000000
P = $46040.52 
algebra 
Steve,
Oops. Monthly deposits.
Let r = 1 + .08/12 = 1.00666666
M (r^480  1)/(r1) = 1000000
3641.007M = 1000000
M = $274.65
Anyone see an error here? 
algebra 
Reiny,
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