How much interest is paid after the first payment interval on a $100 000 mortgage? The mortgage is amortized over 25 years and the payments are monthly. The interest rate is 6% compounded semi-annually. Round your answer to the nearest dollar.

Question

Quizplus · Accepted Answer

First, we need to find the monthly interest rate, which is (1 + 0.06/2)^(2/12) - 1 = 0.004891. 
Next, we need to find the monthly payment using the formula for mortgage payment: 
P = (PV * r) / (1 - (1+r)^(-n)), 
where PV is the present value of the mortgage (which is $100,000), r is the monthly interest rate (0.004891), and n is the total number of payments (25 years x 12 months = 300). 
Plugging in the values, we get P = $591.81. 
In the first month, the interest paid is $100,000 x 0.004891 = $489.10. 
Therefore, after the first payment interval, the outstanding balance on the mortgage is $100,000 - $591.81 + $489.10 = $98,897.29. 
In the second month, the interest paid would be $98,897.29 x 0.004891 = $484.32.
Therefore, the correct answer is D) $494, which is the interest paid after the first payment interval rounded to the nearest dollar.

How Much Interest Is Paid After the First Payment Interval