Question

2. Find the interest rate (to the nearest hundredth) on a $5800 Certificate of Deposit if the interest paid in 9 months is $150.37.

Answer 1

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

$A=P(1+\frac{r}{100})^t$

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, $t=\frac{9}{12}=0.75$

r is the interest rate

Substitute in the formula,

$P+I=P(1+\frac{r}{100})^t$

$5800+150.37=5800(1+\frac{r}{100})^{0.75}$

$5950.37=5800(1+\frac{r}{100})^{0.75}$

$\frac{5950.37}{5800}=(1+\frac{r}{100})^{0.75}$

$1.025=(1+\frac{r}{100})^{0.75}$

Taking log both side,

$\log(1.025)=0.75\log(1+\frac{r}{100})$

$\frac{\log(1.025)}{0.75}=\log(1+\frac{r}{100})$

$0.0142=\log(1+\frac{r}{100})$

Taking exponential both side,

$e^{0.0142}=1+\frac{r}{100}$

$1.014=1+\frac{r}{100}$

$1.014-1=\frac{r}{100}$

$0.014=\frac{r}{100}$

$r=0.014\times 100$

$r=1.4\%$

Multiply it by 12,

$r=1.4\times 12=16.8\%$

Therefore, The interest rate is 16.8%.