#3 of case study:
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 needs to invest annually in order to accumulate a million dollars in the stock market, we can use the concept of compound interest. Compound interest is the interest earned on both the initial investment and the accumulated interest from previous periods.
Here's how to calculate it:
1. Determine the time period: In this case, let's assume Naomi wants to accumulate a million dollars in 10 years.
2. Calculate the annual interest rate: Naomi wants to be conservative, so instead of using the average return of 10%-12%, she decides to use 8%.
3. Use the compound interest formula: The formula to calculate the future value (FV) of an investment with compound interest is:
FV = P * (1 + r)^n,
where:
- FV is the future value (in this case, one million dollars),
- P is the initial investment (the amount Naomi needs to invest annually),
- r is the annual interest rate as a decimal (8% in this case),
- n is the number of compounding periods (in this case, 10).
4. Rearrange the formula: We want to solve for P, so we need to rearrange the formula to isolate P. The formula becomes:
P = FV / (1 + r)^n.
5. Calculate the annual investment amount:
P = 1,000,000 / (1 + 0.08)^10,
= 1,000,000 / 1.08^10,
≈ 1,000,000 / 2.158925,
≈ 463,193.69.
Therefore, Naomi will need to invest approximately $463,194 annually in the stock market to accumulate a million dollars over a 10-year period, assuming an 8% annual interest rate.