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 long Rachel and Richard need to invest their portfolio to reach their retirement goal of $2,100,000, we first calculate their current total portfolio balance. Adding their balances together: \[ \text{Total Portfolio} = \$34,000 + \$125,000 + \$104,000 + \$73,000 + \$84,000 = \$420,000. \] Next, we can use the future value formula for compound interest to calculate the required time. Assuming an annual interest rate \( r \) (which you may need to specify), the future value \( FV \) is given by: \[ FV = PV \times (1 + r)^n, \] where - \( FV \) is the future value (\$2,100,000), - \( PV \) is the present value (\$420,000), - \( r \) is the annual interest rate (expressed as a decimal), and - \( n \) is the number of years. Rearranging this formula to solve for \( n \): \[ n = \frac{\log(FV/PV)}{\log(1 + r)}. \] Substituting the known values: \[ n = \frac{\log(2,100,000 / 420,000)}{\log(1 + r)}. \] Now you can plug in the expected rate of return to find the required number of years. For example, if they expect an average return of 6%: \[ n = \frac{\log(5)}{\log(1.06)} \approx 27.36 \text{ years}. \] So, they would need to invest their portfolio for approximately 27 years to reach their goal, depending on actual market performance. Make sure to round and adjust based on the specific interest rate and any changes in variables you anticipate!