Answer: it will take 7 years for the value of the account to reach $49,300
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 = $41000
A = $49300
r = 2.6% = 2.6/100 = 0.026
n = 12 because it was compounded 12 times in a year.
Therefore,
49300 = 41000(1 + 0.026/12)^12 × t
49300/41000 = (1 + 0.0022)^12t
1.2024 = (1.0022)^12t
Taking log of both sides of the equation, it becomes
Log 1.2024 = 12t × log 1.0022
0.08 = 12 × 0.00095 = 0.0114t
t = 0.08/0.0114
t = 7 years
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