Answer: About 73 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 = 2000
r = 5.5% = 5.5/100 = 0.055
n = 1 because it was compounded once in a year.
A = 100000
Therefore,.
100000 = 2000(1 + 0.055/1)^1 × t
100000/2000 = (1.055)^t
50 = 1.055^t
Taking log of both sides, it becomes
Log 50 = log 1.055^t
1.699 = t × log 1.055
1.699 = 0.0234t
t = 1.699/0.0234
t = 72.6
Approximately 73 years
