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Next question You can retry this question below 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? \( \$ 30,400 \) What was the original amount financed? \( \$ 159,600 \) What is her monthly payment? \( \$ 1,019.40 \) 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. \( \$ 397,384 \)

Ask by Rojas Reed. in the United States
Feb 25,2025

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Down payment: \$30,400 Amount financed: \$159,600 Monthly payment: \$1,019.40 Total spent: \$397,384

Solución

Let's work through the problem step by step. 1. Down Payment:   • Home price = $190,000   • Down payment rate = 16%   • Down payment = 0.16 × $190,000 = $30,400 2. Original Amount Financed:   • Financed amount = Home price – Down payment   • Financed amount = $190,000 – $30,400 = $159,600 3. Monthly Payment:   The monthly payment of a fixed-rate mortgage is calculated using the formula     M = P × [r(1 + r)ⁿ] / [(1 + r)ⁿ – 1]   where:     P = Principal = $159,600     r = monthly interest rate = 6.6%/12 = 0.066/12 ≈ 0.0055     n = total number of payments = 30 × 12 = 360   Plugging in the numbers:     M = 159600 × [0.0055(1 + 0.0055)^(360)] / [(1 + 0.0055)^(360) – 1]   Evaluating this expression gives approximately M ≈ $1,019.40 per month. 4. Total Amount Spent on the Home:   • Total paid on the loan = Monthly payment × Number of payments = $1,019.40 × 360 ≈ $366,984   • Including the down payment: Total = $366,984 + $30,400 = $397,384 Thus, rounding to the nearest cent, the answers are: • Down payment: $30,400 • Original amount financed: $159,600 • Monthly payment: $1,019.40 • Total amount spent (including down payment): $397,384

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The Deep Dive

Did you know that the concept of a mortgage dates back centuries? In ancient Rome, property buyers could take out loans secured against their homes, much like modern mortgages. However, it wasn't until the 1930s that the system as we know it today, complete with long-term loans and fixed interest rates, started to take shape in the United States. This evolution has made homeownership more accessible for millions! When it comes to real-world application, understanding amortization tables can be a game changer! These tables help you see how your payments reduce the loan balance over time. While it can be tempting to focus solely on the monthly payment, knowing how much of each payment goes toward interest versus the principal can empower you to make smarter financial decisions—like paying extra towards the principal to save on interest!

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