How much would you need to deposit in an account now in order to have \( \$ 6000 \) in the account in 15 years? Assume the account earns \( 6 \% \) interest compounded quarterly. Round your answer to the nearest cent.

To find out how much you need to deposit now to reach \( \$6000 \) in 15 years with a quarterly compounded interest rate of \( 6\% \), you can use the formula for compound interest: \[ P = \frac{A}{(1 + r/n)^{nt}} \] Where: - \( A = 6000 \) (the amount you want in the future) - \( r = 0.06 \) (annual interest rate) - \( n = 4 \) (number of times interest is compounded per year) - \( t = 15 \) (number of years) Plugging in the values, we have: \[ P = \frac{6000}{(1 + 0.06/4)^{4 \times 15}} \] Calculating this step by step: 1. \( r/n = 0.06/4 = 0.015 \) 2. \( nt = 4 \times 15 = 60 \) 3. \( (1 + 0.015)^{60} = (1.015)^{60} \approx 2.4596 \) Now substitute all this back into the equation: \[ P = \frac{6000}{2.4596} \approx 2438.58 \] Therefore, you would need to deposit approximately \( \$2438.58 \) now to have \( \$6000 \) in 15 years.