A 10 year $25,430 loan is being paid off with semi-annual payments of $3679.The total interest over the life of the loan is $48,150.What is the outstanding balance of the loan after two years assuming the sum of digits method?

Question

Quizplus · Accepted Answer

Using the sum of digits method, we can find the total number of payments as follows:

Each semi-annual payment is $3679, so the total payment per year is $7358.
The loan is for 10 years, so the total number of payments is 2 payments per year x 10 years = 20 payments.
The sum of digits for 20 payments is 2 + 0 = 2.

Now we can use the outstanding balance formula to find the balance after 2 years:

Outstanding balance after 2 years = Loan amount x (1 + interest rate)^number of payments - Payment amount x ((1 + interest rate)^number of payments - 1) / interest rate

The interest rate can be found by dividing the total interest over the life of the loan by the loan amount and the number of payments:

interest rate = $48,150 / $25,430 / 20 = 0.04727

Plugging in the values we have:

Outstanding balance after 2 years = $25,430 x (1 + 0.04727)^2 - $3,679 x ((1 + 0.04727)^2 - 1) / 0.04727
= $27,681.14

Therefore, the answer is B.

A 10 Year $25,430 Loan Is Being Paid Off with Semi-Annual