Jenelle bought a home for \( \$ 190,000 \), paying \( 16 \% \) as a down payment, and financing the rest at \( 6.6 \% \) interest for 30 years. Round your answers to the nearest cent. How much money did Jenelle pay as a down payment? \( \$ \) What was the original amount financed? \( \$ \) What is her monthly payment? \( \$ \) If Jenelle makes these payments every month for thirty years, determine the total amount of money she will spend on this home. Include the down payment in your answer. \$

To calculate these amounts: 1. **Down Payment**: Jenelle bought a home for \( \$190,000 \) and paid \( 16\% \) as a down payment. \[ \text{Down Payment} = 190,000 \times 0.16 = 30,400 \] Therefore, Jenelle paid a down payment of \( \$30,400 \). 2. **Original Amount Financed**: The amount financed is the purchase price minus the down payment. \[ \text{Amount Financed} = 190,000 - 30,400 = 159,600 \] Thus, the original amount financed is \( \$159,600 \). 3. **Monthly Payment**: To find the monthly payment, we'll use the formula for a fixed-rate mortgage, which is given by: \[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \] where: - \( P = 159,600 \) (principal) - \( r = \frac{0.066}{12} \) (monthly interest rate) - \( n = 30 \times 12 = 360 \) (number of payments) Substituting in the values: \[ r = \frac{0.066}{12} = 0.0055 \] Now plug these into the formula: \[ M = 159600 \times \frac{0.0055(1 + 0.0055)^{360}}{(1 + 0.0055)^{360} - 1} \] After calculating, \( M \approx 1010.21 \). 4. **Total Amount Spent**: The total amount spent on the house is the down payment plus the total payments made. \[ \text{Total Payments} = M \times n = 1010.21 \times 360 \approx 363,076.60 \] Now, add the down payment: \[ \text{Total Amount Spent} = 363,076.60 + 30,400 = 393,476.60 \] So, the final summary is: - Down Payment: \( \$30,400 \) - Original Amount Financed: \( \$159,600 \) - Monthly Payment: \( \$1,010.21 \) - Total Amount Spent: \( \$393,476.60 \)