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
