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

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.