If Naomi invests in a stock portfolio, her returns for 10 or more years will average 10%-12%. Naomi realizes that the stock market has higher returns because it is a more risky investment than a savings account or a CD. She wants her calculations to be conservative so she decides to use 8% to calculate possible stock market earnings. How much will she need to invest annually to accumulate a million dollars in the stock market?
To calculate how much Naomi will need to invest annually to accumulate a million dollars in the stock market, we can use the concept of compound interest. Here's how you can calculate it:
1. Determine the time period: In this case, Naomi wants to accumulate a million dollars in the stock market. However, we need to know the time period over which she plans to invest. Let's assume it's N years.
2. Calculate the future value: To calculate the future value of Naomi's investments, we can use the future value formula for compound interest:
FV = PV * (1 + r) ^ N
where FV is the future value (one million dollars in this case), PV is the present value (the amount Naomi needs to invest annually), r is the annual interest rate (8% in this case), and N is the number of years of investment.
3. Rearrange the formula: To solve for PV (the annual investment amount), we need to rearrange the formula:
PV = FV / ((1 + r) ^ N)
4. Substitute the values: Now, substitute the values into the formula. In this case, FV = $1,000,000, r = 8% (0.08 as a decimal), and we're solving for PV.
PV = $1,000,000 / ((1 + 0.08) ^ N)
Note: The formula assumes that Naomi makes regular annual investments at the start of each period.
By using this formula and adjusting the value of N (the number of years), you can calculate how much Naomi needs to invest annually to accumulate a million dollars in the stock market.