Question

5. Kim Tayes invests $8,000 in a certificate of deposit for 1 year.The certificate earns interest at an annual rate of 4.25%compounded quarterly.a. What is the amount?b. What is the interest earned?c. What is the annual percentage yield to the nearestthousandth of a percent?

Answer 1

The question gives us the following information:

Principal = $8,000

Time = 1 year

Interest rate = 4.25%, compounded quarterly.

We're going to use the following formula to solve the questions:

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

Where A is the total amount at the end of the investment, r is the annual interest rate, n is the number of compounding periods in a year, and t is the time in number of years.

By substituting the given, we get:

`\begin{gathered} A=8,000(1+(0.4025)/(4))^(4(1)) \\ \\ A=8,000(1.010625)^4 \\ \\ A=8,345.4572 \end{gathered}`

Therefore, the amount is $8,345.46.

Interest earned is the additional money received from the investment. So we simply subtract the principal from the total amount.

`\begin{gathered} Interest=8,345.46-8,000 \\ \\ Interest=345.46 \end{gathered}`

So interest is $345.46.

Lastly, to find the annual percentage yield, we divide the interest earned by the principal amount invested.

`\begin{gathered} Yield=(345.46)/(8,000) \\ \\ Yield=0.0431821 \end{gathered}`

The yield is 0.043182 or 4.318%.