Your bank pays \( 8 \% \) interest, compounded quarterly. Use Table \( 12-2 \) to find how much you should deposit now to yield an annuity payment of \( \$ 1,300 \) at the BEGINNING of each three months, for 2 years. Select one: o a. \( \$ 9,713.59 \) b. \( \$ 10,823.13 \) c. \( \$ 9,523.13 \) o d. \( \$ 8,413.59 \)

To find the amount that should be deposited now to yield an annuity payment of $1,300 at the beginning of each three months for 2 years, we can use the formula for the present value of an annuity: \[ PV = \frac{PMT}{r} \left( 1 - \frac{1}{(1 + r)^n} \right) \] where: - \( PV \) is the present value (the amount to be deposited now), - \( PMT \) is the periodic payment (the annuity payment of $1,300), - \( r \) is the interest rate per period (8% per year compounded quarterly, so \( r = \frac{8}{4} = 2\% \) per quarter), - \( n \) is the number of periods (2 years * 4 quarters/year = 8 quarters). Substitute the given values into the formula: \[ PV = \frac{1300}{0.02} \left( 1 - \frac{1}{(1 + 0.02)^8} \right) \] Now, we can calculate the present value using the formula. Calculate the value by following steps: - step0: Calculate: \(\frac{1300}{0.02}\times \left(1-\frac{1}{\left(1+0.02\right)^{8}}\right)\) - step1: Add the numbers: \(\frac{1300}{0.02}\times \left(1-\frac{1}{1.02^{8}}\right)\) - step2: Convert the expressions: \(\frac{1300}{0.02}\times \left(1-\frac{1}{\left(\frac{51}{50}\right)^{8}}\right)\) - step3: Simplify: \(\frac{1300}{0.02}\times \left(1-\frac{50^{8}}{51^{8}}\right)\) - step4: Subtract the numbers: \(\frac{1300}{0.02}\times \frac{51^{8}-50^{8}}{51^{8}}\) - step5: Divide the numbers: \(65000\times \frac{51^{8}-50^{8}}{51^{8}}\) - step6: Multiply: \(\frac{65000\left(51^{8}-50^{8}\right)}{51^{8}}\) - step7: Multiply: \(\frac{65000\times 51^{8}-65000\times 50^{8}}{51^{8}}\) The present value (the amount to be deposited now) is approximately $9,523.13. Therefore, the correct answer is: c. $9,523.13