Question

You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate of 4% per year and is compounded monthly, how long does it take until you have $3,000 without depositing any additional funds? 121.862 years 12.1862 years 10.155 years 1.0155 years

Answer 1

Answer: 10.155

Step-by-step explanation: got it right on the test

Answer 2

10.153 years

Explanation:

The future value of such an investment is given by ...

FV = P·(1 +r/12)^(12t)

where P is the principal invested, FV is the future value of it, r is the annual interest rate, and t is the number of years.

Dividing by P and taking the log, we have ...

FV/P = (1 +r/12)^(12t)

log(FV/P) = 12t·log(1 +r/12)

Dividing by the coefficient of t gives ...

t = log(FV/P)/log(1 +r/12)/12 = log(3000/2000)/log(1 +.003333...)/12 ≈ 121.842/12

t ≈ 10.153 . . . years