At age 5, how much would you have to save per month to have $1 million in your account at age 65, if your investment rate was 10% per year? Assume no taxes and compounding on a monthly basis.
To calculate how much you need to save per month to have $1 million in your account at age 65, with an investment rate of 10% per year, compounded monthly, you can use the formula for future value of an annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = future value (desired amount, in this case $1 million)
P = monthly savings amount
r = monthly interest rate (10% per year divided by 12 months = 0.83%)
n = number of compounding periods (60 years multiplied by 12 months = 720 months)
Now, let's substitute the values into the formula and solve for P:
$1,000,000 = P * ((1 + 0.0083)^720 - 1) / 0.0083
To solve this equation, we can rearrange it and isolate P on one side:
P = $1,000,000 * 0.0083 / ((1 + 0.0083)^720 - 1)
Using a calculator or a spreadsheet software, you can calculate this expression to find the monthly savings amount needed to reach $1 million by age 65.