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Reil [10]
3 years ago
12

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.
Mathematics
1 answer:
gregori [183]3 years ago
4 0

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%.

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