Question

Joe Jay purchased a new colonial home for $260,000, putting down 20%. He decided to use Loyal Bank for his mortgage. They were offering a 6 1/2% for a 25-year mortgage. The principal after the first payment had a balance outstanding of:

A. $207,270.95


B. $207,720.59


C. $207,720.95


D. $207,270.59

Answer 1

The principal after the first payment on Joe Jay's mortgage is $206,065.82.

Step-by-step explanation:

To find the principal balance after the first payment, we need to calculate the amount that is paid off with the first payment. The principal balance is the original purchase price minus the down payment. In this case, Joe Jay purchased a house for $260,000 and put down 20%, which means he paid $260,000 * 0.20 = $52,000 as a down payment. So, the principal balance is $260,000 - $52,000 = $208,000.

Next, we need to calculate the monthly mortgage payment. The mortgage rate is 6 1/2%, which can be expressed as a decimal as 0.065. The loan term is 25 years, which is equivalent to 300 months. We can use the formula for calculating the monthly payment of a mortgage:

Monthly Payment = Principal Balance * (Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Number of Months)))

Using the given values, the monthly payment is $208,000 * (0.065 / (1 - (1 + 0.065)^(-300))) = $1,934.18.

To find the balance outstanding after the first payment, we subtract the monthly payment from the principal balance:

Balance Outstanding = Principal Balance - Monthly Payment = $208,000 - $1,934.18 = $206,065.82.

Therefore, the correct answer is $206,065.82, which is option D.

Answer 2

My solution to the problem is as follows:

260000 *20%=52000 ao rest maount=208000

now 6.5% for 25%

now P=208000 and rate 6.5%

apply

p×(1+r/100)−x(1+r/100)
where x is instalment

You can now get the answer from the choices given after solving for x

I hope my answer has come to your help. God bless and have a nice day ahead!