Answer: the person must leave the money for 13.4 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,
A = $8200
P = $4500
r = 4.5% = 4.5/100 = 0.045
n = 12 because it was compounded 12 times in a year.
Therefore,
8200 = 4500(1 + 0.045/12)^12 × t
8200/4500 = (1 + 0.00375)^12t
1.8222 = (1.00375)^12t
Taking log of both sides,
Log 1.8222 = 12t × log 1.00375
0.261 = 12t × 0.001626
0.261 = 0.019512t
t = 0.261/0.019512
t = 13.4 years
