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

The interest rate is 16.8%.

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+(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=(9)/(12)=0.75`

r is the interest rate

Substitute in the formula,

`P+I=P(1+(r)/(100))^t`

`5800+150.37=5800(1+(r)/(100))^(0.75)`

`5950.37=5800(1+(r)/(100))^(0.75)`

`(5950.37)/(5800)=(1+(r)/(100))^(0.75)`

`1.025=(1+(r)/(100))^(0.75)`

Taking log both side,

`\log(1.025)=0.75\log(1+(r)/(100))`

`(\log(1.025))/(0.75)=\log(1+(r)/(100))`

`0.0142=\log(1+(r)/(100))`

Taking exponential both side,

`e^(0.0142)=1+(r)/(100)`

`1.014=1+(r)/(100)`

`1.014-1=(r)/(100)`

`0.014=(r)/(100)`

`r=0.014* 100`

`r=1.4\%`

Multiply it by 12,

`r=1.4* 12=16.8\%`

Therefore, The interest rate is 16.8%.