Carrie earned $3673 from a summer job and put it in a savings account that earns 10% interest compounded annually. When Carrie started college, she had $7614 in the account which she used to pay her tuition. How long was the money in the account?

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,

A = 7614

r = 10% = 10/100 = 0.1

n = 1 because it was compounded once in a year.

P = 3673

Therefore,

7614 = 3673 (1+0.1/1) ^1 * t

7614/3673 = 1.01^t

2.073 = 1.01^t

Taking log of both sides, it becomes

Log 2.073 = log 1.01^t

0.3166 = t * 0.0043

t = 0.3166/0.0043

t = 73.3