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.
.
.
.
Question content area top right
Part 1
Beginning Balance
$85,000
Term
20 years
Initial index rate
5.3%
Margin
2.7%
Adjustment period
1 year
Adjusted index rate
6.8%
*Adjusted balance
$83,203.43
What is the initial monthly payment?
To calculate the initial monthly payment, we need to use the formula for an adjustable rate mortgage:
Initial Monthly Payment = (Adjusted Balance * (Adjusted Index Rate + Margin)) / (1 - (1 + Adjusted Index Rate)^(-Term))
Plugging in the given values:
Adjusted Balance = $83,203.43
Adjusted Index Rate = 6.8%
Margin = 2.7%
Term = 20 years
Initial Monthly Payment = ($83,203.43 * (6.8% + 2.7%)) / (1 - (1 + 6.8%)^(-20))
Calculating the expression:
Initial Monthly Payment = ($83,203.43 * 9.5%) / (1 - (1 + 6.8%)^(-20))
Next, we need to convert the percentages into decimal form:
Initial Monthly Payment = ($83,203.43 * 0.095) / (1 - (1 + 0.068)^(-20))
Calculating the value inside the parentheses:
Initial Monthly Payment = ($7,894.33) / (1 - (1 + 0.068)^(-20))
Next, we calculate the expression inside the second set of parentheses:
Initial Monthly Payment = ($7,894.33) / (1 - (1.068)^(-20))
Calculating the exponent:
Initial Monthly Payment = ($7,894.33) / (1 - 0.37689)
Next, we calculate the subtraction inside the parentheses:
Initial Monthly Payment = ($7,894.33) / (0.62311)
Finally, we can solve for the initial monthly payment:
Initial Monthly Payment ≈ $12,665.07
Therefore, the initial monthly payment is approximately $12,665.07.
To find the initial monthly payment of the adjustable-rate mortgage (ARM), we need to consider the principal balance, loan term, initial index rate, and the margin.
Given:
Principal Balance: $85,000
Term: 20 years
Initial Index Rate: 5.3%
Margin: 2.7%
To calculate the initial monthly payment, follow these steps:
Step 1: Calculate the total interest rate by adding the initial index rate and the margin:
Total Interest Rate = Initial Index Rate + Margin
Total Interest Rate = 5.3% + 2.7%
Total Interest Rate = 8%
Step 2: Convert the term of the loan from years to months:
Loan Term in months = Loan Term in years x 12
Loan Term in months = 20 years x 12
Loan Term in months = 240 months
Step 3: Use the following formula to calculate the initial monthly payment:
Initial Monthly Payment = (Principal Balance * Total Interest Rate) / (1 - (1 + Total Interest Rate)^(-Loan Term in months))
Using the given values:
Initial Monthly Payment = ($85,000 * 8%) / (1 - (1 + 8%)^(-240))
Calculating this using a calculator or spreadsheet, the initial monthly payment amounts to approximately $654.13.
Therefore, the initial monthly payment for this adjustable rate mortgage (ARM) is approximately $654.13.
To find the initial monthly payment of an adjustable rate mortgage (ARM), you will need the principal balance, the term, the initial index rate, and the margin.
In this case, the principal balance is $85,000, the term is 20 years, the initial index rate is 5.3%, and the margin is 2.7%.
To calculate the initial monthly payment, you can use the following formula:
Montly Payment = (Principal Balance * (Monthly Interest Rate)) / (1 - (1 + Monthly Interest Rate) ^ (-Total Number of Payments))
First, convert the annual interest rate to a monthly interest rate. Divide the initial index rate by 12, and convert it to a decimal by dividing it by 100.
Monthly Interest Rate = 5.3% / 12 / 100 = 0.0044166667
Now, substitute the values into the formula:
Monthly Payment = ($85,000 * 0.0044166667) / (1 - (1 + 0.0044166667) ^ (-20 * 12))
Calculate the exponent part first:
(1 + 0.0044166667) ^ (-20 * 12) ≈ 0.40758625
Now, substitute it back into the formula:
Monthly Payment = ($85,000 * 0.0044166667) / (1 - 0.40758625)
Simplify the equation:
Monthly Payment ≈ $377.07
Therefore, the initial monthly payment for this adjustable rate mortgage is approximately $377.07.