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): $38,000

Government bond mutual fund​ (GB): $135,000

Large capital mutual fund​ (LC): $104,000

Small capital mutual fund​ (SC): $72,000

Real estate trust fund​ (RE) : $89,000 Rachel and Richard believe they need at least $2,200,000 to retire. The money market account grows at 3.0% annually, the government bond mutual fund grows at 5.5% annually, the large capital mutual fund grows at 10.5% 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 $2,200,000 goal?

Rachel and Richard will need to invest their accounts for ______ or more years to reach $2,200,000. ​(Round to the nearest whole​ number.)

Answer 1

Fv = PV*(1+r)^n

We need to find n

Total FV = FV of MM + FV of Gb + FV of LC + FV of SC + FV of RE

2200,000= 38000*1.03^n + 135000*1.055^n + 104000*1.105^n+ 72000*1.135^n + 89000*1.03^n

We use scenario analysis to solve this in excel

Solving for n = 19.5535 rounded off to 20 years

Hence invest for 20 years to reach $ 2200,000

WORKINGS