Question

Your principal is $800. The annual rate of interest is 5.5%. What is the interest after 6 months?

Answer 1

$311.94

Explanation:

We have that the compound interest is given by the following equation:

`A=P\cdot(1+(r)/(t))^(n\cdot t)`

In this case, we know that the principal is 800, the interest is 5.5%, and the value of n is 12, since the equivalence between year and months is that there are 12 months in a year and time is 6 months.

Therefore, we replace and calculate:

`\begin{gathered} A=800\cdot(1+(0.055)/(12))^(12\cdot6) \\ A=800\cdot1.00458^(72) \\ A=800\cdot1.38991 \\ A=1111.94 \end{gathered}`

The value of A would be the value of the total debt, the interests would be the subtraction between that total and the principal, therefore:

`\begin{gathered} I=1111.94-800 \\ I=311.94 \end{gathered}`

Interest in 6 months would be $311.94