Question

quiz content
prior to completing this \quick check\ quiz, make sure you have completed the associated learning activities and practices exercises in the module.
now that you have gone through the learning activities, lets take a quick practice quiz to make sure you understand the basic ideas. this practice quiz has three (3) multiple-choice questions and is worth two (2) points. there is a 15 - minute time limit. practice showing correct and complete work on scrap paper as you complete these problems.
question 1
0.66 points
jesse invests $8000 in a cd for 3 years at a nominal rate of 4% compounded semiannually. calculate the compound interest, based on the future value formula.
a $1009.30
b $960.00
c $9009.30
d $8960.00
question 2
0.67 points

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is \(A = P(1+\frac{r}{n})^{nt}\), where \(P\) is the principal amount, \(r\) is the annual interest rate (in decimal form), \(n\) is the number of times interest is compounded per year, and \(t\) is the number of years. The compound interest \(I=A - P\).

Given \(P=\$8000\), \(r = 4\%=0.04\), \(n = 2\) (compounded semiannually), and \(t = 3\) years.

Step2: Calculate the value of \((1+\frac{r}{n})^{nt}\)

First, calculate \(\frac{r}{n}=\frac{0.04}{2}=0.02\) and \(nt=2\times3 = 6\). Then \((1+\frac{r}{n})^{nt}=(1 + 0.02)^{6}\).
Using the formula \((a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}\) or a calculator, \((1.02)^{6}\approx1.126162\).

Step3: Calculate the amount \(A\)

Substitute into the formula \(A=P(1+\frac{r}{n})^{nt}\). So \(A = 8000\times(1.02)^{6}\approx8000\times1.126162=\$9009.30\).

Step4: Calculate the compound interest \(I\)

\(I=A - P\). Substitute \(A=\$9009.30\) and \(P = 8000\). Then \(I=9009.30-8000=\$1009.30\).

Answer:

A. \(\$1009.30\)