Answer: it will take 20.6 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 = $37900
P = $10000
r = 6.75% = 6.75/100 = 0.0675
n = 12 because it was compounded 12 times in a year.
Therefore,
37900 = 10000(1 + 0.065/12)^12 × t
37900/10000 = (1 + 0.00542)^12t
3.79 = (1.00542)^12t
Taking log of both sides, it becomes
Log 3.79 = 12t × log 1.00542
0.579 = 12t × 0.00234752004
0.579 = 0.02817t
t = 0.579/0.02817
t = 20.6 years
