Answer: 13.6 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 = $11300
r = 6% = 6/100 = 0.06
n = 12 because it was compounded 12 times in a year.
Therefore,.
11300 = 5000(1 + 0.06/12)^12 × t
11300/5000 = (1 + 0.005)^12t
2.26 = (1.005)^12t
Taking log of both sides, it becomes
Log 2.26 = 12tlog 1.005
0.354 = 12t × 0.0022
0.354 = 0.0264t
t = 0.354/0.026
t = 13.6 years
