Respuesta :
Answer:
The interest rate is 16.8%.
Step-by-step explanation:
Given : On a $5800 Certificate of Deposit if the interest paid in 9 months is $150.37.
To find : The interest rate?
Solution :
The formula to find the interest rate is
[tex]A=P(1+\frac{r}{100})^t[/tex]
Where, A is the amount A=P+I
I is the interest I=$150.37
P is the principal P=$5800
t is time t=9 months
In year, [tex]t=\frac{9}{12}=0.75[/tex]
r is the interest rate
Substitute in the formula,
[tex]P+I=P(1+\frac{r}{100})^t[/tex]
[tex]5800+150.37=5800(1+\frac{r}{100})^{0.75}[/tex]
[tex]5950.37=5800(1+\frac{r}{100})^{0.75}[/tex]
[tex]\frac{5950.37}{5800}=(1+\frac{r}{100})^{0.75}[/tex]
[tex]1.025=(1+\frac{r}{100})^{0.75}[/tex]
Taking log both side,
[tex]\log(1.025)=0.75\log(1+\frac{r}{100})[/tex]
[tex]\frac{\log(1.025)}{0.75}=\log(1+\frac{r}{100})[/tex]
[tex]0.0142=\log(1+\frac{r}{100})[/tex]
Taking exponential both side,
[tex]e^{0.0142}=1+\frac{r}{100}[/tex]
[tex]1.014=1+\frac{r}{100}[/tex]
[tex]1.014-1=\frac{r}{100}[/tex]
[tex]0.014=\frac{r}{100}[/tex]
[tex]r=0.014\times 100[/tex]
[tex]r=1.4\%[/tex]
Multiply it by 12,
[tex]r=1.4\times 12=16.8\%[/tex]
Therefore, The interest rate is 16.8%.
