Question 1178497: The Trissel family agreed on a price of $223,600 for a home. Their company credit union offers a 5.9% 20 year loan with 15% down, resulting in a monthly payment of $1350.71. Find the monthly payment for the Trissels if they choose a 15 year loan instead of 20 with the same APR and down payment. How much would they save overall?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this problem step-by-step:
**1. Calculate the Down Payment and Loan Amount**
* Down payment: $223,600 * 15% = $33,540
* Loan amount: $223,600 - $33,540 = $190,060
**2. Calculate the Monthly Payment for a 15-Year Loan**
We'll use the loan payment formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]
Where:
* M = Monthly payment
* P = Principal loan amount ($190,060)
* i = Monthly interest rate (annual rate / 12)
* n = Total number of payments (years * 12)
Calculations:
* Annual interest rate: 5.9% = 0.059
* Monthly interest rate (i): 0.059 / 12 ≈ 0.00491667
* Number of payments (n): 15 years * 12 months/year = 180 months
Now, plug the values into the formula:
M = 190060[ 0.00491667(1 + 0.00491667)^180 ] / [ (1 + 0.00491667)^180 - 1]
M = 190060[ 0.00491667(2.4419) ] / [ 2.4419 - 1]
M = 190060[ 0.012055 ] / [ 1.4419]
M = 190060[0.0083606]
M = $1588.99
Therefore the monthly payment will be approximately $1588.99
**3. Calculate the Total Amount Paid for Each Loan**
* 20-year loan: $1350.71/month * 240 months = $324,170.40
* 15-year loan: $1588.99/month * 180 months = $286,018.20
**4. Calculate the Total Interest Paid for Each Loan**
* 20-year loan interest: $324,170.40 - $190,060 = $134,110.40
* 15-year loan interest: $286,018.20 - $190,060 = $95,958.20
**5. Calculate the Overall Savings**
* Savings in total amount paid: $324,170.40 - $286,018.20 = $38,152.20
* Savings in total interest paid: $134,110.40 - $95,958.20 = $38,152.20
**Answers:**
* The monthly payment for a 15-year loan would be approximately $1588.99.
* The Trissels would save $38,152.20 overall by choosing the 15 year loan.
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