Question

You decide to put $175 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 3% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds? 8.0111 years 96.1332 years 93.2914 years 94.8377 years

Answer 1

First, determine the annual effective interest based on the annual interest and the compounding,
                                ieff = (1 + i/m)^m - 1
Substituting,
                       ieff = (1 + 0.03/12)^12 - 1 = 0.0304
To determine the future worth (F) of the current investment (P) is,
                                    F = P(1+ieff)^n
Substituting all the known values with n unknown,
                               3000 = 175(1 + 0.0304)^n
Solving for n gives an n = 94.8867 years
Among the choices, the nearest value is 94.8377 years.