Question

You decide to put $150 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2.5% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?

10.1101 years
119.954 years
121.321 years
134.34 years

Answer 1

The formula is
A=p (1+r/k)^kt
3000=150 (1+0.025/12)^12t
Solve for t
3000/150=(1+0.025/12)^12t
Take the log
Log (3000/150)=12t×log (1+0.025/12)
12t=Log (3000/150)÷log (1+0.025/12)
T=[Log (3000/150)÷log (1+0.025/12)]÷12
T=(log(3,000÷150)÷log(1+0.025÷12))÷12
T=119.954 years