The table shows the specifications of an adjustable rate mortgage (ARM). Assume no caps apply. Find a) the initial monthly payment; b) the monthly payment for the second adjustment; and c) the change in monthly payment at the first adjustment.
*The principal balance at the time of the first rate adjustment.
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Part 1
Beginning Balance
$
Term
20 years
Initial index rate
%
Margin
%
Adjustment period
1 year
Adjusted index rate
%
*Adjusted balance
$
To determine the initial monthly payment for an adjustable rate mortgage (ARM), you would need the following information:
- Principal balance: This is the original amount borrowed for the mortgage.
- Term: The length of time for the mortgage, in this case, 20 years.
- Initial index rate: This is the starting interest rate based on the index it is tied to.
- Margin: The additional interest added to the index rate to determine the overall interest rate.
- Adjustment period: The frequency at which the interest rate adjusts, in this case, every 1 year.
- Adjusted index rate: The index rate after the first adjustment period.
- Adjusted balance: The principal balance at the time of the first rate adjustment.
Without the specific values for these variables, it is not possible to calculate the initial monthly payment, the monthly payment for the second adjustment, or the change in monthly payment at the first adjustment.
To calculate the initial monthly payment for the adjustable rate mortgage (ARM), you will need the following information:
1. Beginning Balance: $
2. Term: 20 years
3. Initial index rate: %
4. Margin: %
5. Adjustment period: 1 year
6. Adjusted index rate: %
7. Adjusted balance: $
a) To find the initial monthly payment, follow these steps:
Step 1: Calculate the adjusted index rate by adding the initial index rate and the margin.
Adjusted index rate = Initial index rate + Margin
Step 2: Calculate the monthly interest rate by dividing the adjusted index rate by 12 (as there are 12 months in a year).
Monthly interest rate = Adjusted index rate / 12
Step 3: Calculate the number of monthly payments by multiplying the term (in years) by 12.
Number of monthly payments = Term (in years) x 12
Step 4: Use the formula for calculating the monthly payment for an adjustable rate mortgage:
Monthly payment = (Adjusted balance x Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of monthly payments))
Substitute the values into the formula to find the initial monthly payment.
b) To find the monthly payment for the second adjustment, you would follow the same steps as above, but with an updated adjusted balance.
c) To find the change in the monthly payment at the first adjustment, you would subtract the initial monthly payment from the monthly payment for the second adjustment.
Please provide the values for the beginning balance, initial index rate, margin, adjusted index rate, and adjusted balance, so that I can calculate the answers for you.
To find the initial monthly payment, we need to calculate the monthly payment using the initial index rate and margin.
a) Initial Monthly Payment:
1. Take the adjusted balance and divide it by the term in months (20 years equals 240 months). This gives us the principal balance at the time of the first rate adjustment.
2. Add the adjusted index rate (expressed as a decimal) to the margin rate (also expressed as a decimal).
3. Multiply this sum by the principal balance at the time of the first rate adjustment.
4. Divide the result by 12 to get the monthly payment.
b) Monthly Payment for the Second Adjustment:
To calculate the monthly payment for the second adjustment, you would follow the same steps as above, using the adjusted balance from the first adjustment as the new principal balance.
c) Change in Monthly Payment at the First Adjustment:
To find the change in monthly payment at the first adjustment, you would compare the monthly payment calculated in the first step with the monthly payment calculated in the second step. The difference between these two payments represents the change in the monthly payment.
Please provide the specific values for the adjusted index rate, margin, and adjusted balance in order to calculate the exact values for parts a), b), and c).