You would like to invest some money today such that your investment will be worth $100,000 fifteen years from now. Your broker gives you two options. First, you can invest in a GIC account and earn a guaranteed annual rate of 4%. Alternatively, you can invest in stocks and hope to earn an average of 7% per year. How much more will you have to invest today if you opt for the GIC account rather than the stocks?

To solve this problem, we need to calculate the present value of an investment that would grow to $100,000 in 15 years under two different interest rates: 4% for the GIC account and 7% for the stock investment. The present value (PV) is calculated using the formula:

\[
PV = \frac{FV}{(1 + r)^n}
\]

where:
- $ PV $ is the present value (the amount you need to invest today),
- $ FV $ is the future value (the amount you want the investment to grow to),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of years.

### 1. **For the GIC Account:**
Given:
- $ FV = 100,000 $ dollars,
- $ r = 4\% = 0.04 $,
- $ n = 15 $ years.

\[
PV_{\text{GIC}} = \frac{100,000}{(1 + 0.04)^{15}} = \frac{100,000}{(1.04)^{15}}
\]

### 2. **For the Stock Investment:**
Given:
- $ FV = 100,000 $ dollars,
- $ r = 7\% = 0.07 $,
- $ n = 15 $ years.

\[
PV_{\text{Stock}} = \frac{100,000}{(1 + 0.07)^{15}} = \frac{100,000}{(1.07)^{15}}
\]

Let's calculate both values.### Results:
- **Present Value for GIC Account**: \$55,526.45
- **Present Value for Stock Investment**: \$36,244.60
- **Difference**: \$19,281.85

This means that if you opt for the GIC account with a 4% interest rate, you would need to invest **\$19,281.85 more** today compared to investing in stocks with an expected 7% annual return, in order to reach $100,000 in 15 years.

Would you like more details or have any questions? 

Here are some related questions you might consider:
1. How does the difference in present values change with different time horizons?
2. What would the future value be if I invested a fixed amount today at either rate?
3. What are the risks associated with choosing a stock investment over a GIC account?
4. How does compounding frequency affect the required initial investment?
5. What if I expect a different annual return from the stock investment?
6. How would inflation impact the future value of the investment?
7. What happens if the interest rates change during the investment period?
8. How would taxes on the returns affect the required initial investment?

**Tip**: When choosing between investments, consider both the potential returns and the associated risks, especially over long periods.

Compare investments to reach $100,000 in 15 years: Guaranteed Investment Certificate (GIC) at 4% vs stocks at 7%. Calculate how much more you need to invest today for each option.

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