Question

Sandra earned $8,000.00 from a summer job and put it in a savings account that earns 3% interest compounded continuously. When Sandra started college, she had $8,327.00 in the account which she used to pay for tuition. How long was the money in the account? Round your answer to the nearest month.
____ years and ____ months

Answer 1

Answer: 1 year and 4 months

Step-by-step explanation:

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

P = 8000

r = 3% = 3/100 = 0.03

A = 8327

Therefore,

8327 = 8000 x 2.7183^(0.03 x t)

8327/8000 = 2.7183^(0.03t)

1.040875 = 2.7183^(0.03t)

Taking log of both sides, it becomes

Log 1.040875 = log 2.7183^(0.03t)

0.0174 = 0.03tlog2.7183

0.0174 = 0.03t × 0.434 = 0.01302t

t = 0.0174/0.01302

t = 1.336

0.336 × 12 = 4.032

Therefore, the money waa in the account for 1 year and 4 months