Mr. Brown and Ms. Brown agreed to pay $560,000 for a four-bedroom colonial home in Massachusetts...

Mr. Brown and Ms. Brown agreed to pay $560,000 for a four-bedroom colonial home in Massachusetts with a $60,000 down payment. They have a 30-year mortgage at a fixed rate of 6.0%.

How much is their monthly payment?

After their first payment, what would be the balance of the principal?

Expert Solution

We are given the following information:

MonthlyPayment	PMT	To be calculated
Rate of interest	r	6.00%
Number of years	n	30.00
Monthly	frequency	12.00
Loan amount	PV	500000.00

We need to solve the following equation to arrive at the required PMT:

So the monthly payment is 2997.75

Below is the impact of the first payment:

Month	Opening Balance	PMT	Interest	Principal repayment	Closing Balance
1	$ 5,00,000.00	$ 2,997.75	$ 2,500.00	$ 497.75	$ 4,99,502.25

Opening balance = previous year's closing balance
Closing balance = Opening balance+Loan-Principal repayment
PMT is calculated as per the above formula
Interest = 0.06 /12 x opening balance
Principal repayment = PMT - Interest
So after first payment, the principal amount repaid is $497.75 and the remaining loan balance is 499502.25

jeff jeffy answered 1 year ago

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