Answer: the interest rate is 4.86%
Explanation:
Assuming the interest was compounded annually, 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 = $350000
A = $1450000
n = 1 because it was compounded once in a year.
t = 30 years
Therefore,.
1450000 = 350000(1+r/1)^1 × 30
1450000/350000 = (1 + r)^30
4.14 = (1 + r)^30
Taking log of both sides of the equation, it becomes
Log 4.14 = 30 log(1 + r)
0.617 = 30 log (1 + r)
0.0206 = log(1 + r)
Taking exponent of both sides, it becomes
10^0.0206 = 10^log(1 + r)
1 + r = 1.0486
r = 1.0486 - 1 = 0.0486
Converting to percentage, it becomes
r = 0.0486 × 100 = 4.86%