.I know how to set it up and all but Im not getting any of my answer choices!?

Question

You decide to put $100 in a savings account for $3000 downpayment on a new car.

If the account has an interest rate of 2% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?

Answer 1

Compound interest formula is given by:

P = principal amount = 100

i = interest rate = 2% = 0.02 per year

y = number of years

n = number of compounding periods per year = 12

FV = future value = 3000

FV = P*(1+i/n)^y*12

3000 = 100*(1+0.02/12)y*12

y = log(30)/log(1.0016667)/12 = 170yrs