Question

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): $37,000 Government bond mutual fund (GB): $150,000 Large capital mutual fund (LC): $103,000 Small capital mutual fund (SC): $77,000 Real estate trust fund (RE): $86,000 Rachel and Richard believe they need at least $2,100,000 to retire. The money market account grows at 1.5% annually, the government bond mutual fund grows at 5.0% annually, the large capital mutual fund grows at 9.0% annually, the small capital mutual fund grows at 13.5% annually, and the real estate trust fund grows at 3.0% annually. With the assumption that no more funds will be deposited into any of these accounts, how long will it be until they reach the $2,100,000 goal? Rachel and Richard will need to invest their accounts for or more years to reach $2,100,000.

Answer 1

The future value of Rachel and Richard's portfolio will be calculated using compound interest for each account with varying growth rates, and we can estimate the time it will take to reach their retirement goal by iterative computation or using financial tools.

Step-by-step explanation:

To determine when Rachel and Richard's portfolio will be sufficient for them to retire, we need to calculate the future value of each investment component, taking into account individual growth rates, and then find out how long it takes for the total to reach their goal of $2,100,000. We can use the formula of compound interest to calculate the future value of each account: FV = P(1 + r)n, where P is the principal amount, r is the annual growth rate, and n is the number of years.

Since we do not have an explicit formula to directly solve for n, and the rates are different for each account, this involves either iterative computation or using financial functions in a spreadsheet or financial calculator to estimate the time until the portfolio's total value meets the retirement goal.

Given the power of compound interest, an essential strategy is to start saving early, as exemplified by the retirement savings examples provided. These illustrate how initial investments grow over time, highlighting the importance of early and consistent savings for achieving retirement goals,