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?

A. 10.1101 years
B. 119.954 years
C. 121.321 years
D. 134.34 years

Answer 1

B.) 119.954 years

Answer 2

Principal amount deposited in a savings account = $150
Final amount of money needed = $3000
Percentage of interest = 2.5%
Let us assume the time taken = t years
Then
A = P (1 + r/n) ^ nt
3000 = 150(1 +0.025/12)^t
3000 = 150 * (1 + 0.002083)^t
(1.002083)^t = 20
Taking log on both sides we get
log (1.002083)^t = log 20
t * ln(1.002083) = ln(20)
t = ln(20)/ln(1.002083)
= 1439.68
= 119.973 years
From the above deduction we can easily conclude that the correct option among all the options that are given in the question is the second option or option "B".