Question

If an investment of $8000 accumulates to $8400 in seven and a half years, the annual simple interest rate is:

Answer 1

Answer:

the annual interest rate is 0.67%

Step-by-step explanation:

Amount invested = $8000

Future value = $8400

time = 7 1/2 yeras

rate = ?

To answer the question, we will apply the simple interset formula:

`\begin{gathered} I\text{ = P}* R* T \\ P\text{ = principal = 8000} \\ R\text{ = ?} \\ T\text{ = time = 7}(1)/(2) \\ I\text{ = interest = ?} \end{gathered}`
`\begin{gathered} Future\text{ value = Principal + interest} \\ 8400\text{ = 8000 + interest} \\ Interest\text{ = 8400 - 8000} \\ Interest\text{ = 400} \end{gathered}`

substitute the values into the simple interest formula to get r:

`\begin{gathered} 400\text{ = 8000}* r*7(1)/(2) \\ 400\text{ = 8000}* r*(15)/(2) \\ 400\text{ = 60000r} \\ r\text{ = 400/60000} \\ r\text{ = 0.0067} \end{gathered}`

In percentage, the annual interest rate is 0.67%