In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.
How much must you invest each month in a mutual fund yielding 12.6% compounded monthly to become a millionaire in 10 years?
P(1 + .126/12)^120 - 1)/(.126/12) = 1,000,000
P = ...
To calculate the monthly investment required to become a millionaire in 10 years, we need to use the formula for the future value of an ordinary annuity:
A = P * [(1 + r)^n - 1] / r
Where:
A = Future value (in this case, $1,000,000)
P = Monthly investment
r = Annual interest rate (12.6%/12 for monthly compounding)
n = Number of compounding periods (12 months * 10 years = 120 months)
To solve for P, we can rearrange the formula:
P = A * (r / [(1 + r)^n - 1])
Now let's calculate the monthly investment required to become a millionaire in 10 years with a mutual fund yielding 12.6% compounded monthly:
A = $1,000,000
r = 12.6% / 12 = 0.105
n = 120 months
P = $1,000,000 * (0.105 / [(1 + 0.105)^120 - 1])
You can plug in these values into a calculator or spreadsheet software to compute the result.
Note: It is important to consider that investment returns are not guaranteed and can vary over time.