Marcia has $ 220,000 saved for her retirement... (Finance problem)?

Marcia has $ 220,000 saved for her retirement. How long will it take for the investment to double in value if it earns 7% compounded monthly? Measure the period in years. A. 13.9 years B. 7.6 years C. 9.9 years D. 9.0 years

Public Comments

1. F = P(1 + r/n)^(Yn) F = future value = $440,000 P = principal value = $220,000 r = annual interest rate = 7% n = monthly periods per year = 12 Y = number of years = unknown F = P(1 + r/n)^(Yn) $440,000 = $220,000(1 + 7%/12)^(Y*12) 440,000 = 220,000(1 + 0.07/12)^(Y*12) Convert the 1 to 12/12 before adding. 440,000 = 220,000(12/12 + 0.07/12)^(Y*12) 440,000 = 220,000(12.07/12)^(Y*12) Divide both sides of the equal sign by 220,000 440,000/220,000 = (12.07/12)^(Y*12) 2 = (12.07/12)^(Y*12) Take the log of both sides of the equal sign. log(2) = log(12.07/12)^(Y*12) log(2) = 12Y * log(12.07/12) Divide both sides of the equal sign by log(12.07/12) log(2)/log(12.07/12) = 12Y * log(12.07/12)/log(12.07/12) log(2)/log(12.07/12) = 12Y Divide both sides of the equal sign by 12 Y = log(2)/12log(12.07/12) You have enough information to finish this on your own. When I work it out all the way, I do obtain one of the four answers you posted above.