# Interest percentage from selling price or cost price

(c.p= cost price, s.p= selling price)

I was doing a problem and I got its interest rate wrong.

problem: An item when sold at 212.5, interest got is 12.5 . So what is the interest percentage?

My solution:
s.p=212.5 , interest=12.5
s.p=100 , interest= 12.5/212.5 *100 = 5.88%

Book solution:
c.p=212.5 - 12.5 = 200

c.p=200 , interest= 12.5
c.p=100 , interest= 12.5/200 * 100 = 6.25%

What is it on percentage, that my understanding is wrong.

Mentallic
Homework Helper
Work this backwards. Say you were to sell the item at $200 but there is a 6.25% interest rate of that cost which is$12.50, so you then need to sell it with this interest price included, so $212.50. This makes sense, right? You get the customer to pay that extra tax, so you include it on top of the cost price. Hence to figure it out, you need to remove the interest from the sell price to get the cost price, then figure out what the interest is based on that cost price. Hence to figure it out, you need to remove the interest from the sell price to get the cost price, then figure out what the interest is based on that cost price. i.e to say, to calculate interest, we always take interest from the cost price and cannot be interest achieved from selling price i.e we cannot calculate interest, considering the product sold at 100$.

Mentallic
Homework Helper
One thing I don't understand is the following:

My solution:
s.p=212.5 , interest=12.5
s.p=100 , interest= 12.5/212.5 *100 = 5.88%
What is that part in red? Why is the sell price both 212.5 and 100? That makes no sense. You've done it 3 times now.

Anyway, you most definitely can calculate the interest, as the book had done.

One thing I don't understand is the following:
What is that part in red? Why is the sell price both 212.5 and 100? That makes no sense. You've done it 3 times now.

When the sell price is 212.5, interest is 12.5 . So when sell price is 100, interest = 12.5/212.5 * 100.

Mentallic
Homework Helper
When the sell price is 212.5, interest is 12.5 . So when sell price is 100, interest = 12.5/212.5 * 100.

You do realize that the part in red is done merely to turn the interest (as a number that's equal to 12.5/212.5 = 0.0588) into a percentage (equal to 0.0588*100% = 5.88%).
When the sell price is 100, then the interest is $5.88 because the interest rate is 5.88%, so we calculate 100*5.88% = 100*(5.88/100) = 5.88. When the sell price is 100, then the interest is$5.88 because the interest rate is 5.88%, so we calculate 100*5.88% = 100*(5.88/100) = 5.88.
This my question, why can't we take selling price as 100, to get the interest rate.

Is it, we always take the interest percent from the cost price(=100) only and not from the selling price.

Mentallic
Homework Helper
Because of the fact that the interest of the cost price was added to the cost price to give you the selling price. So to find that interest, you need to figure out the cost price first, because that's where the interest came from.

jbriggs444
Homework Helper
Is it, we always take the interest percent from the cost price(=100) only and not from the selling price.

One answer is that it is a matter of convention.

10% interest on a starting amount of 100 would be 10 for a final amount of 110. Start with 100, end with 110 at 10% interest.
10% interest on an ending amount of 110 would be 11 for an initial amount of 99. Start with 99, end with 110 at 10% interest.

It is difficult to do business when the lender and the borrower cannot agree on what "10 percent" means. So one meaning is chosen and the other is discarded. The conventional choice is that interest is quoted on the starting balance. [This is a good choice since the amount that changes hands at the start of a loan is often fixed and the amount that will be repaid at the end of the loan is a quantity that may be haggled over]

One answer is that it is a matter of convention.

10% interest on a starting amount of 100 would be 10 for a final amount of 110. Start with 100, end with 110 at 10% interest.
10% interest on an ending amount of 110 would be 11 for an initial amount of 99. Start with 99, end with 110 at 10% interest.

It is difficult to do business when the lender and the borrower cannot agree on what "10 percent" means. So one meaning is chosen and the other is discarded.

Thanks, this is what, I wanted to be sure.