Respuesta :
Answer:
The continuous yearly interest is 22.5% per year.
Step-by-step explanation:
Continuous yearly interest:
Continuous yearly interest is defined as the sum of the interest comes from principle and the interest comes from interest.
The formula for continuous interest yearly is
[tex]A=Pe^{rt}[/tex]
where A = The final amount =$110,000
P= principle =$4,700
r= rate of interest
t= time (in year)= 14 years
[tex]\therefore 110,000= 4,700e^{r\times 14}[/tex]
[tex]\Rightarrow e^{14r}= \frac{110,000}{4,700}[/tex]
Taking ln both sides
[tex]\Rightarrow ln e^{14r}= ln(\frac{110,000}{4,700})[/tex]
[tex]\Rightarrow {14r}= ln(\frac{1100}{47})[/tex]
[tex]\Rightarrow r=\frac{ln( \frac{1100}{47})}{14}[/tex]
[tex]\Rightarrow r = 0.225[/tex] (approx)
The continuous yearly interest is 0.225 = 22.5% per year.
