Question 8 of 15 . Step 1 of 1 Emilia and Liam are purchasing a home. They wish to save money for 10 years and purchase a house that has a value of \( \$ 190,000 \) with cash. If they deposit money into an account paying \( 4 \% \) interest. compounded monthly, how much do they need to deposit each month in order to make the purchase? Round your answer to the nearest cent, if necessary. Formulas Answer How to enter your answer fopens in new window) Keypad Keyboard Shortcuts

To accumulate \( \$190,000 \) in 10 years with a savings account that offers \( 4\% \) interest compounded monthly, Emilia and Liam can use the future value of an ordinary annuity formula: \( FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \), where \( FV \) is the future value, \( P \) is the monthly deposit, \( r \) is the monthly interest rate, and \( n \) is the total number of deposits. Here, \( r = \frac{0.04}{12} = 0.003333 \) and \( n = 10 \times 12 = 120 \). By rearranging this formula to solve for \( P \), they find they need to deposit around \( \( 1,473.36 \) each month to reach their goal. Pretty impressive planning for their future home! Did you know that the concept of compounding goes back centuries? The term "compounding" comes from finance practices in ancient cultures, particularly in Babylonian and Roman times where interest was often applied to loans. These societies understood the value of investments, setting the stage for our modern savings behavior. How fascinating is that?