Answer: the interest rate is 6%
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 = $3900
A = $9200
t = 14 years
n = 365 because it was compounded 365 times in a year.
Therefore,
9200 = 3900(1 + r/365)^365 × 14
9200/3900 = (1 + 0.0027274r)^5110
2.359 = (1.0027274r)^5110
Taking log of both sides of the equation,it becomes
Log 2.359 = 5110 log (1 + 0.0027274r)
0.373 = 5110 log (1 + 0.0027274r)
0.373/5110 = log (1 + 0.0027274r)
0.000073 = log (1 + 0.0027274r)
Taking inverse log of both sides of the equation, it becomes
10^0.000073 = 10^log (1 + 0.0027274r)
1.000168 = 1 + 0.0027274r
0.0027274r = 1.000168 - 1
0.0027274r = 0.000168
r = 0.000168/0.0027274
r = 0.06
r = 0.06 × 100 = 6%
