Future value of a portfolio. Rachel and Richard want to know when their current

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): $39,000 Government bond mutual fund (GB): $130,000 Large capital mutual fund (LC): $107,000 Small capital mutual fund (SC): $73,000 Real estate trust fund (RE): $87,000 Rachel and Richard believe they need at least $2,500,000 to retire. The money market account grows at 1.5% annually, the government bond mutual fund grows at 6.0% annually, the large capital mutual fund grows at 9.5% annually, the small capital mutual fund grows at 13.5% annually, and the real estate trust fund grows at 5.0% 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 $2,500,000 goal? Rachel and Richard will need to invest their accounts for or more years to reach $2,500,000. (Round to the nearest whole number)

Explanation / Answer

Soln ; Let T be the time period till that period they need to get invested to reach $2500000

We can say that 39000*(1.015)T + 130000*(1.06)T + 107000*(1.095)T + 73000*1.135T + 87000* 1.05T = 2500000

We can do the hit and trial in excle using these values in excel and automated the function

We will get the following result keeping 21 years (approx.) as the years to remain invested to reach goal of $2500000

Investment 39000 130000 107000 73000 87000 Rate 1.015 1.06 1.095 1.135 1.05 C = Inv *rate^T 53315.17606 441940.69 719575.45 1042870.668 242377.5628 Sum of C 2500079.552

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