Answer:
• The future value is $635.72
,
• The compound interest is $75.72.
Explanation:
To find the future value at compound interest, we use the formula below:
[tex]A(t)=P(1+\frac{r}{k})^{nk}\text{ where }\begin{cases}P=\text{Principal Invested} \\ r=\text{Interest Rate} \\ k=\text{Number of compounding periods}\end{cases}[/tex]
Given:
• Principal, P= $560
,
• Rate, r = 4.25% =0.0425
,
• Period, k = 4 (Quarterly)
,
• Time, n = 3 years
Substitute these values into the formula:
[tex]\begin{gathered} A(t)=560(1+\frac{0.0425}{4})^{4\times3} \\ A(t)=\$635.72 \end{gathered}[/tex]
The future value is $635.72
Next, we find the compound interest:
[tex]\begin{gathered} Interest=Future\text{ Value-Principal} \\ =635.72-560 \\ =\$75.72 \end{gathered}[/tex]
The compound interest is $75.72.
