Final Answer:
d. The monthly payment for the mortgage, excluding escrowed taxes and insurance, is approximately $726.
e. The total cost of interest over 30 years amounts to around $160,160.
Step-by-step explanation:
Given:
Home price = $114,000
Down payment requirement = 20%
Three points at closing
Mortgage term = 30 years
Fixed-rate = 6.5%
a. Required down payment:
20% of the home price = 0.20 * $114,000 = $22,800
b. Amount of the mortgage:
Home price - Down payment = $114,000 - $22,800 = $91,200
c. Cost for the three points at closing:
Three points = 3% of the mortgage amount = 0.03 * $91,200 = $2,736
d. Monthly payment (excluding escrowed taxes and insurance):
To calculate the monthly payment (PMT), use the formula:
PMT = P * r * (1 + r)ⁿ / ((1 + r)ⁿ - 1)
Where:
P = Principal amount = $91,200
r = Monthly interest rate = Annual interest rate / 12 months = 6.5% / 12 = 0.0054167
n = Number of payments = 30 years * 12 months = 360 payments
PMT = $91,200 * 0.0054167 * (1 + 0.0054167)³⁶⁰ / ((1 + 0.0054167)³⁶⁰ - 1)
PMT ≈ $726 (rounded to the nearest dollar)
e. Total cost of interest over 30 years:
Total Interest = (Monthly Payment * Number of Payments) - Principal Amount
Total Interest = ($726 * 360) - $91,200
Total Interest ≈ $160,160 (rounded to the nearest dollar)
Therefore, the monthly payment for the mortgage (excluding escrowed taxes and insurance) is approximately $726, and the total cost of interest over 30 years amounts to around $160,160.
Complete Question
Use PMT- to determine the regular payment amount, rounded to the nearest dollar. The price of a home is $114,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 6.5%. Complete parts (a) through (e) below a. Find the required down payment $ 22800 b. Find the amount of the mortgage S91200
c. How much must be paid for the three points at closing? $ 2736 (Round to the nearest dollar as needed) Use PMT=- to determine the regular payment amount, rounded to th down payment and three points at the time of closing. The cost of the home is financed below. c. How much must be paid for the three points at closing? S 2736 (Round to the nearest dollar as needed.)
d. Find the monthly payment (excluding escrowed taxes and insurance). $ (Round to the nearest dollar as needed.). e. Find the total cost of interest over 30 years. $ (Round to the nearest dollar as needed.)