21. You deposit \( \$ 10,000 \) in an accouml that pays \( 1.49 \% \) interest compounded quarterly, a. Find the future value after one year. Round to the nearest cent. b. Use the future value formula for simple interest to determine the effective annual yield. Round to the nearest hundredth of a percent.

To find the future value after one year with quarterly compounding interest, you can use the formula: \[ FV = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( P = 10,000 \) (the principal) - \( r = 0.0149 \) (annual interest rate as a decimal) - \( n = 4 \) (number of times that interest is compounded per year) - \( t = 1 \) (the number of years) Plugging in these values, we get: \[ FV = 10,000 \left(1 + \frac{0.0149}{4}\right)^{4 \times 1} \approx 10,000 \times 1.003725 \approx 10,037.25 \] So, the future value after one year is approximately \( \$10,037.25 \). For the effective annual yield using the simple interest formula, the formula is: \[ EAY = \left(1 + \frac{r}{n}\right)^{n} - 1 \] Again with \( r = 0.0149 \) and \( n = 4 \): \[ EAY = \left(1 + \frac{0.0149}{4}\right)^{4} - 1 \approx (1.003725)^{4} - 1 \approx 0.015033 \] To convert this to a percentage, multiply by 100: \[ EAY \approx 1.50\% \] Therefore, the effective annual yield is approximately \( 1.50\% \).