QQuestionMathematics
QuestionMathematics
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Part 1
Use
PMT=Prn^1−1 +rn−nt
to determine the regular payment amount, rounded to the nearest dollar.The price of a home is
$340,000.
The bank requires a
5%
down payment. After the down payment, the balance is financed with a
15-year
fixed-rate mortgage at
7%.
Determine the monthly mortgage payment (excluding escrowed taxes and insurance) to the nearest dollar."
12 months agoReport content
Answer
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Step 1:: Calculate the down payment amount.
Down payment $$ = 0.05 imes $340,000 = $17,000
The bank requires a 5% down payment, so we need to find 5% of $340,000:
Step 2:: Calculate the amount to be financed.
Financed amount $$ = $340,000 - $17,000 = $323,000
The financed amount is the home price minus the down payment:
Step 3:: Determine the number of payments (n).
For a 15 -year fixed-rate mortgage, there will be 15 years imes 12 months = 1$ payments: n = 1$
Step 4:: Determine the interest rate (r) per payment period.
The annual interest rate is 7%, so the monthly interest rate is: r = 0.07 imes (1 / 12) = 0.005833333333333333
Step 5:: Calculate the regular payment amount (PMT) using the formula:
PMT = Prn1−1+rn−n = $323,000 imes 0.006924260644658815 ≈ $2,379.01
PMT = Prn^1−1 +rn−nt where: P = Financed amount = $323,000 r = Monthly interest rate = 0.005833333333333333 n = Number of payments = 180 First, calculate 1 - (1 + r)^-n: 1 - (1 + 0.005833333333333333)^- 180 ≈ 0.006924260644658815 Now, calculate PMT: Rounded to the nearest dollar, the monthly mortgage payment is $2,379.
Final Answer
The monthly mortgage payment is $2,379.
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