Answer :
Answer: 13.29%
Step-by-step explanation:
The formula to calculate the compound amount (compounded continuously) is given by :-
[tex]A=Pe^{rt}[/tex], where P is the principal amount , r is the rate of interest ( in decimal) and t is the time period.
Given : P= $ 35,000 , A= $257,000 and t=15 years
To find : r , we substitute all the values in the above formula , we get
[tex]257000=(35000)e^{15r}\\\\\Rightarrow\ e^{15r}=\dfrac{257000}{35000}\\\\\Rightarrow\ e^{15r}=7.3428[/tex]
Taking natural log on both the sides , we get
[tex]15r=\ln(7.3428)\\\\\Rightarrow\ 15r=1.9937\\\\\Rightarrow\ r=\dfrac{1.9937}{15}0.132913333333\approx0.1329=13.29\%[/tex]
Hence, the annual interest rate = 13.29%