Answer: it will take 18.4 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 = $1000
A = $4000
n = 1 because it was compounded once in a year.
t = 12 years
Therefore,.
4000 = 1000(1 + r/1)^1 × 12
4000/1000 = (1 + r)^12
4 = (1 + r)^12
Log 4 = 12 log (1 + r)
0.602/12 = log (1 + r)
0.0501 = log (1 + r)
Taking inverse log of both sides, it becomes
10^0.0501 = 10^log(1 + r)
1.122 = 1 + r
r = 1.122 - 1 = 0.122
At r = 0.122 and A = 8000
Therefore,
8000/1000 = (1 + r)^1 × t
8 = (1 + 0.122)^t
8 = (1.122)^t
Log 8 = tlog 1.122
0.903 = 0.049 × t = 0.049t
t = 0.903/0.049
t = 18.4 years
