ett college predicts that in 18 years it will take \( \$ 350,000 \) to attend the college for four years. Madison has a substantial amount of cash and wishes to invest a lump mof money for her child's college fund. How much should Madison put aside in an account with an APR of \( 7 \% \) compounded monthly in order to have \( \$ 350,000 \) in the count in 18 years? Round your answer to the nearest cent, if necessary. Formulas

To determine how much Madison needs to invest now to accumulate $350,000 in 18 years at an APR of 7% compounded monthly, she can use the future value formula: \[ FV = PV \times (1 + r/n)^{nt} \] Where: - \( FV \) is the future value ($350,000), - \( PV \) is the present value (the amount Madison needs to invest), - \( r \) is the annual interest rate (0.07), - \( n \) is the number of times interest is compounded per year (12 for monthly), - \( t \) is the number of years (18). Rearranging the formula to solve for \( PV \): \[ PV = \frac{FV}{(1 + r/n)^{nt}} \] Substituting the known values into the formula will give the amount Madison needs to set aside today. By substituting \( FV = 350,000 \), \( r = 0.07 \), \( n = 12 \), and \( t = 18 \), Madison can calculate the precise amount she needs to invest. For a smoother transition into practicality, understand that starting a college fund early means taking advantage of the power of compound interest. Even small monthly contributions can add up over time, so don't hesitate if the lump sum amount feels daunting! Each investment creates potential growth, leading to a comfortable college fund when the time arrives.