Not yet answered Points out of 10.00 p Flag question Nevada takes out a loan of \( \$ 8,000 \), at \( 7 \% \) interest, for 48 months. Find the maturity value. Select one: O. \( \$ 560 \) ob. \( \$ 10,240 \) O.c. \( \$ 26,880 \) o d. \( \$ 11.67 \)

To find the maturity value of the loan, we can use the formula for calculating the future value of a loan: \[ FV = PV \times (1 + r)^n \] Where: - \( FV \) is the future value (maturity value) of the loan - \( PV \) is the present value (initial loan amount) of the loan - \( r \) is the annual interest rate - \( n \) is the number of years the loan is taken for Given: - Present value (PV) = $8,000 - Annual interest rate (r) = 7% = 0.07 - Number of years (n) = 48 months = 4 years Substitute the given values into the formula: \[ FV = 8000 \times (1 + 0.07)^4 \] Now, we can calculate the maturity value. Calculate the value by following steps: - step0: Calculate: \(8000\left(1+0.07\right)^{4}\) - step1: Add the numbers: \(8000\times 1.07^{4}\) - step2: Convert the expressions: \(8000\left(\frac{107}{100}\right)^{4}\) - step3: Simplify: \(8000\times \frac{107^{4}}{100^{4}}\) - step4: Rewrite the expression: \(1000\times 8\times \frac{107^{4}}{100^{4}}\) - step5: Rewrite the expression: \(10^{3}\times 8\times \frac{107^{4}}{10^{8}}\) - step6: Reduce the numbers: \(8\times \frac{107^{4}}{10^{5}}\) - step7: Rewrite the expression: \(8\times \frac{107^{4}}{2^{5}\times 5^{5}}\) - step8: Rewrite the expression: \(2^{3}\times \frac{107^{4}}{2^{5}\times 5^{5}}\) - step9: Reduce the numbers: \(1\times \frac{107^{4}}{2^{2}\times 5^{5}}\) - step10: Multiply: \(\frac{107^{4}}{12500}\) The maturity value of the loan is approximately $10,486.37. Therefore, the correct answer is: b. $10,240