Answer: it take 13.09 years to double your money.
Step-by-step explanation:
Assuming the interest was compounded annually, 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 = P
A = 2P
r = 5.5% = 5.5/100 = 0.055
n = 1 because it was compounded once in a year.
Therefore,.
2P = P(1 + 0.055/1)^1 × t
2P = P(1.055)^t
2P/P = 1.055^t
2 = 1.055^t
Taking log of both side, it becomes
Log2 = tlog1.055.
0.301 = 0.023t
t = 0.301/0.023
t = 13.09 years
