find the compound interest and future value. round your answers to the nearest cent. do not round…

Explanation:

Step1: Identify compound interest formula

The formula for compound future value is: $$A = P\left(1 + \frac{r}{n}\right)^{nt}$$ Where:

• $A$ = future value,
• $P = 530$ (principal),
• $r = 0.0475$ (annual interest rate),
• $n = 4$ (compounded quarterly),
• $t = 2$ (time in years)

Step2: Calculate periodic rate & total periods

Periodic rate: $\frac{r}{n} = \frac{0.0475}{4} = 0.011875$ Total compounding periods: $nt = 4 \times 2 = 8$

Step3: Compute future value

$$A = 530\left(1 + 0.011875\right)^{8}$$ $$A = 530\left(1.011875\right)^{8}$$ $$A \approx 530 \times 1.099447$$ $$A \approx 582.71$$

Step4: Calculate compound interest

Compound interest = Future Value - Principal $$I = A - P = 582.71 - 530 = 52.71$$

Answer:

The future value is $$582.71$, and the compound interest is $$52.71$.