Question

A business owes $8000 on a loan. Every month, the business pays 12 of the amount remaining on the loan.

How much will the business pay in the sixth month?

Answer 1

The business will pay $506.99 on the loan in the sixth month, after making monthly payments of 12% of the remaining balance on an $8000 loan.

Step-by-step explanation:

To determine how much the business will pay in the sixth month on a loan where they pay off 12% of the remaining balance each month, we need to use a decay formula. This is a type of exponential decay since the amount owed is decreasing by a fixed percentage each month. The formula to find the remaining balance after each payment is:

Balance after n payments = Initial amount * (1 - rate)^n

Starting with an initial loan amount of $8000 and a monthly payment rate of 12% (or 0.12 in decimal form), we calculate the remaining balance each month until the sixth month:

1. Month 1: 8000 * (1 - 0.12) = 8000 * 0.88 = $7040 remaining
2. Month 2: 7040 * 0.88 = $6195.20 remaining
3. Month 3: 6195.20 * 0.88 = $5455.78 remaining
4. Month 4: 5455.78 * 0.88 = $4801.09 remaining
5. Month 5: 4801.09 * 0.88 = $4224.96 remaining
6. Month 6: 4224.96 * 0.88 = $3717.97 remaining

Now we can find out how much will be paid in the sixth month by calculating 12% of the balance at the end of the fifth month:

Sixth month payment = 12% of 4224.96
Sixth month payment = 0.12 * 4224.96
Sixth month payment = $506.99
The business will pay $506.99 in the sixth month.

Answer 2

Here is the answer to the given problem above. Given that the business owes $8000 on a loan and every month, it pays 1212. So for the first month, the remaining is 6,788. On the second month is 5,576, and on the third month, it is 4,364. In the fourth month, the remaining would be 3,152, and in the fifth month is 1,940. Therefore, on the sixth month, if the business pays 1,212 still, the remaining would be $728 only. Hope this answer helps.