Answer:
3.97%
Explanation:
You want to know the annual interest rate, compounded daily, that will result in $43,000 growing to $75,000 in 14 years.
Formula
The formula for the account value is ...
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r compounded n times per year for t years.
Application
Filling in the given values, we can solve for r.
75000 = 43000(1 +r/365)^(365·14)
75/43 = (1 +r/365)^5110 . . . . . divide by 43000 and reduce the fraction
Taking the 1/5110 power gives ...
(75/43)^(1/5110) = 1 +r/365 ≈ 1.00010886855
r/365 = 0.0010886855 . . . . subtract 1
r = 0.001086855·365 . . . . . multiply by 365
r ≈ 0.039737 = 3.9737%
The required interest rate is about 3.97%.