Carmen is acing for a new car that costs $15,000. If she puts $5000 in an account that earns 6% compounded monthly, how long will it take her to save enough money to buy the car?

Answer: it will take 18 years

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P (1+r/n) ^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 5000

A = 15000

r = 6% = 6/100 = 0.06

n = 12 because it was compounded 12 times in a year.

Therefore,.

15000 = 5000 (1+0.06/12) ^12 * t

15000/5000 = (1.005) ^12t

3 = (1.005) ^12t

Taking the log of both sides,

Log 3 = log (1.005) ^12t

0.4771 = 12t log1.005 = 12t * 0.0022

0.0264t = 0.4771

t = 0.4771/0.0264t

t = 18

6 year