Answer: it will take 43.25 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 = $10450
r = 5.5% = 5.5/100 = 0.055
n = 2 because it was compounded 2 times in a year.
Therefore,.
10450 = 1000(1 + 0.055/2)^2 × t
10450/1000 = (1 + 0.0275)^2t
10.45 = (1.0275)^2t
Taking log of both sides, it becomes
Log 10.45 = 2t log 1.0275
1.019 = 2t × 0.01178 = 0.02356t
t = 1.019/0.02356
t = 43.25 years
