Question 1173150: Darrell Frye is planning to buy an office building at a cost of $989,000. He must pay 10% down and has a choice of financing terms. He can select from a 9% 30-year loan and pay 4 discount points, a 9.25% 30-year loan and pay 3 discount points, or a 9.5% 30-year loan and pay 2 discount points. Darrell expects to hold the building for two years and then sell it. Except for the three rate and discount point combinations, all other costs of purchasing and selling are fixed and identical.
If Darrell chooses the 4-point 9% loan, what will be his total outlay in points and payments after 24 months?
I got the amount financed = $890,100
I'm having trouble getting the total outlay for the 4-point 9% loan.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down Darrell Frye's loan options and calculate his total outlay for the 9% loan with 4 discount points.
**1. Calculate the Down Payment:**
* Down payment = 10% of $989,000 = $98,900
**2. Calculate the Loan Amount:**
* Loan amount = $989,000 - $98,900 = $890,100
**3. Calculate the Cost of Discount Points:**
* Discount points = 4% of $890,100 = $35,604
**4. Calculate the Monthly Payment for the 9% Loan:**
* We'll use the mortgage payment formula:
* M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]
* Where:
* M = Monthly payment
* P = Principal loan amount ($890,100)
* i = Monthly interest rate (9% / 12 = 0.75% or 0.0075)
* n = Total number of payments (30 years * 12 months/year = 360 months)
* M = $890,100 [ 0.0075(1 + 0.0075)^360 ] / [ (1 + 0.0075)^360 - 1]
* M = $890,100 [ 0.0075(15.9085) ] / [ 15.9085 - 1]
* M = $890,100 [ 0.11931375 ] / [ 14.9085 ]
* M = $890,100 * 0.00800313
* M = $7,123.69 (approximately)
**5. Calculate the Total Payments After 24 Months:**
* Total payments = $7,123.69 * 24 = $170,968.56
**6. Calculate the Total Outlay:**
* Total outlay = Cost of discount points + Total payments
* Total outlay = $35,604 + $170,968.56 = $206,572.56
**Therefore, if Darrell chooses the 4-point 9% loan, his total outlay in points and payments after 24 months will be approximately $206,572.56.**
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