Question

Jon Ericson bought a home with a 11.5% adjustable rate mortgage for 20 years. He paid $10.67 monthly per thousand on his original loan.
At the end of 2 years he owes the bank $50,000. Now that interest rates have gone up to 13%, the bank will renew the mortgage at this rate or Jon can pay $50,000.
Jon decides to renew and will now pay $11.72 monthly per thousand on his loan. You can ignore the small amount of principal that has been paid.

What is the amount of the old monthly payment? $ ____
What is the amount of the new monthly payment? $ ____
What is the percent of increase in his new monthly payment? ____ %

Answer 1

Remark

The first fact you need to know is that the bank has taken money from you and nothing has been reduced from the principle. Crafty people those bankers; you are going to pay off the interest before touching the principle. They're like you to refinance for the rest of your life at the rates you currently have.

Point. You started out with a 50k debt. You still have that same debt.

Solution

Givens

number of thousands (n) = 50000/1000 = 50

Amount paid per thousand (A) = 10.67

Total monthly payments (T) = ?

Part A

T = n * A

T = 50 * 10.67

T = 533.50 is the old monthly payment

Part B

T = n * A

T = 50 * 11.72

T = 586.00  new monthly payment.

Part C

This is a notes question. What have you been told in your notes on this question. You can find the raw amount just by subtracting 586 - 533.50 = 52.50

But how do you find the % increase. Which one of the payments do you use as your base?

In point of fact, you should be using the first number 533.5

What % will you get when you multiply that by 533.5 and get 52.50?

You are not trying to find 586. You are trying to find the number that you add to 533.5 to get to 586

The answer is (52.50 / 533.5)*100% = 9.84% is the % increase.

Answer 2

You are told to ignore the amount of principal paid, so you are apparently to assume the loan amount was for $50 thousand.

a) The old monthly payment was $10.67×50 = $533.50

b) The new monthly payment is $11.72×50 = $586.00

c) The increase in monthly payment is figured in the usual way:

... (new/old -1)×100% = (1.0984-1)×100% = 9.84%

_____

In reality, about 3% of the loan will have been paid at the end of 2 years. Thus, the original loan amount may have been near $51,500. This problem is telling you to ignore the difference.