You are 18 now. You want to have one million dollars when you are 45. How much do you need to save each month, at 10 percent to have your million dollars at age 45?
Where are you getting 10 percent interest? Is that interest compounded yearly, monthly or ??
It is compounded monthly.
To calculate the amount you need to save each month to accumulate one million dollars by the time you turn 45, you can use the concept of future value of money. The formula for future value of money is:
FV = PV * (1 + r/n)^(n*t)
Where:
FV represents the future value of the investment
PV represents the present value or initial amount invested
r represents the annual interest rate as a decimal
n represents the number of times the interest is compounded per year
t represents the number of years
In your case, you want to save one million dollars by the time you are 45, assuming an interest rate of 10%, with a monthly contribution. Let's break it down:
PV: The present value is currently zero since you are starting from scratch.
FV: You want to accumulate one million dollars.
r: The annual interest rate is 10%, so we need to convert it to decimal form, which is 0.10.
n: The interest is compounded annually. Since you want to make monthly contributions, you need to compound it 12 times per year.
t: The time period is 45 - 18 = 27 years.
Using the formula mentioned earlier, we can rearrange it to solve for PV:
PV = FV / (1 + r/n)^(n*t)
PV = 1000000 / (1 + 0.10/12)^(12*27)
Now, you have the present value (PV), which is the amount you need to accumulate by saving each month.
To calculate the monthly contribution, you can rearrange the formula to solve for PV:
PV = contribution_amount * ((1 + r/n)^(n*t) - 1) / (r/n)
In this case, PV is the one million dollars, r is 0.10, n is 12, and t is 27.
1000000 = contribution_amount * ((1 + 0.10/12)^(12*27) - 1) / (0.10/12)
Now, you can solve this equation to find the monthly contribution amount:
contribution_amount = 1000000 * (0.10/12) / ((1 + 0.10/12)^(12*27) - 1)
Using a calculator or a spreadsheet application, you can evaluate the right side of the equation to find the monthly contribution amount.