Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have \( \$ 25,000 \) after 10 years with an APR of \( 6 \% \) compounded quarterly. Round your answer to the nearest cent, if necessary. Formulas

To calculate the present value (PV) of money, you can use the formula: \[ PV = \frac{FV}{(1 + r/n)^{nt}} \] Where: - \( FV \) is the future value, which is \( \$25,000 \) - \( r \) is the annual interest rate (as a decimal), so \( 6\% = 0.06 \) - \( n \) is the number of times interest is compounded per year, which is \( 4 \) for quarterly - \( t \) is the number of years the money is invested or borrowed, which is \( 10 \) Now, substituting the values into the formula: \[ PV = \frac{25000}{(1 + 0.06/4)^{4 \times 10}} \] Calculating \( r/n \): \[ r/n = 0.06/4 = 0.015 \] Calculating \( nt \): \[ nt = 4 \times 10 = 40 \] Now calculate \( (1 + r/n)^{nt} \): \[ (1 + 0.015)^{40} \approx (1.015)^{40} \approx 1.8061 \] Now substitute back into the PV formula: \[ PV = \frac{25000}{1.8061} \approx 13819.74 \] Therefore, you need to invest approximately \( \$13,819.74 \) now to reach \( \$25,000 \) after 10 years at an APR of \( 6\% \) compounded quarterly.