Future value of a portfolio. Rachel and Richard want to know when their current portfolio will be sufficient for them to retire. They have the following balances in their portfolio: Money market account (MM): \( \$ 34,000 \) Government bond mutual fund \( (\mathrm{GB}): \$ 125,000 \) Large capital mutual fund (LC): \( \$ 104,000 \) Small capital mutual fund (SC): \( \$ 73,000 \) Real estate trust fund (RE): \( \$ 84,000 \) Rachel and Richard will need to invest their accounts for \( \square \) or more years to reach \( \$ 2,100,000 \). (Round to the nearestlwhole number.)

To determine how many years Rachel and Richard need to invest their current portfolio to reach \$2,100,000, we'll use the **Future Value (FV)** formula for compound interest: \[ FV = PV \times (1 + r)^n \] Where: - \( PV \) = Present Value (\$420,000) - \( FV \) = Future Value (\$2,100,000) - \( r \) = Annual interest rate - \( n \) = Number of years Since the problem doesn't specify the interest rates for each account, we'll assume an **average annual return**. For a diversified portfolio like theirs, a reasonable average annual return might be **7%**. **Step-by-Step Calculation:** 1. **Set Up the Equation:** \[ 2,100,000 = 420,000 \times (1 + 0.07)^n \] 2. **Divide Both Sides by \$420,000:** \[ 5 = (1.07)^n \] 3. **Take the Natural Logarithm of Both Sides:** \[ \ln(5) = n \times \ln(1.07) \] 4. **Solve for \( n \):** \[ n = \frac{\ln(5)}{\ln(1.07)} \approx \frac{1.6094}{0.0677} \approx 23.78 \] 5. **Round to the Nearest Whole Number:** \[ n \approx 24 \text{ years} \] **Conclusion:** Rachel and Richard will need to invest their current portfolio for **24 years** to reach \$2,100,000, assuming an average annual return of **7%**. **Note:** The actual number of years may vary based on the specific interest rates of each investment component in their portfolio. If different rates are applicable, a more detailed calculation considering each account's growth rate would be necessary.