A corporation takes out a $100,000 loan to be repaid over 6-years with quarterly payments of $5591.28 at j₄ = 10%.The total interest to be paid on the loan over the 6 years is $34,190.72 Under the sum of digits method,what is the outstanding balance after 10 payments?

Question

Quizplus · Accepted Answer

Using the sum of digits method, we first calculate the sum of the digits from 1 to 24 (6 years x 4 quarters per year):

1 + 2 + 3 + ... + 24 = (24 x 25)/2 = 300

Next, we calculate the portion of the total interest attributed to each payment. This is done by dividing each quarterly payment into the total interest:

$34,190.72 / 24 = $1,424.61

We can then calculate the balance after 10 payments using the formula:

Outstanding balance = Principal - (Payment - Interest) x Remaining term factor

For the first payment, the remaining term factor is simply 24 (i.e. all 24 payments remain). For the second payment, it is 23, and so on.

Using this formula, we get:

Outstanding balance = $100,000 - ($5,591.28 - $1,424.61) x (24 + 23 + ... + 15)

Outstanding balance = $66,311.05 (rounded to the nearest cent)

Therefore, the best choice is B, with an outstanding balance of $66,311.

A Corporation Takes Out a $100,000 Loan to Be Repaid