Your ARM contract is $100,000,monthly payments for 30 years.Your contract rates are 4.50% and 6%,respectively,for the first two years.What is the balance of the loan at the end of year two?

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the amortization formula to calculate the balance of the loan at the end of year two.

We know that the contract rate for the first year is 4.50%, so the monthly interest rate is 0.045/12 = 0.00375. Similarly, the contract rate for the second year is 6%, so the monthly interest rate is 0.06/12 = 0.005.

Let's calculate the total number of payments for the first two years:

For the first year: 12 months x $100,000 x 0.00375 = $3,750
For the second year: 12 months x $100,000 x 0.005 = $6,000

So the total payments made in the first two years is $9,750. Let's subtract this amount from the total amount owed at the beginning of the loan:

$100,000 - $9,750 = $90,250

Now, we need to calculate the balance of the loan at the end of year two. We can use the amortization formula:

Balance = P(1 + r)^n - (PMT x (((1 + r)^n - 1)/r))

where:

P = the principal amount (in this case, $90,250)
r = the monthly interest rate (0.005)
n = the total number of payments made (24, since we're calculating this at the end of year two)
PMT = the monthly payment amount

We don't know the monthly payment amount, but we can calculate it using a loan calculator or spreadsheet program. Using a loan calculator, we find that the monthly payment for a 30-year loan at 4.5% is $507.07.

Now we can plug in the values into the formula:

Balance = $90,250(1 + 0.005)^24 - ($507.07 x (((1 + 0.005)^24 - 1)/0.005))
Balance = $97,088.14

Therefore, the balance of the loan at the end of year two is $97,088 rounded to the nearest dollar, which corresponds to choice C.

Your ARM Contract Is $100,000,monthly Payments for 30 Years