# Calculate the reverse percentage if total is unknown

Lets say, I'll get 100.000 USD in 30 days, but I need most of the money now. I find a (possibly weird) bank who offers me 1.25% interest for these 30 days, which is \$1250. So they pay me 98.750 USD now and I'll have to repay 100.000 USD in 30 days - everyone is happy with the deal.

However, one day before I have to pay back the money to the bank I loose all my memory. I see the transfer of 98.750 USD and I have the offer with the interest rate of 1.25%, but I don't remember neither the 1250 USD nor the full 100.000 USD. How do I calculate the interest amount (the total is easy from there)?

98.750 * 0.0125 = 1234.375 is obviously wrong. ;-)

The money that you have is $$100-1.25=98.75$$ Percent of the original.
Therefore you divide $$98750$$ dollars by $$0.9875$$ to get your total of $$100,000$$ dollars.
In actuality they only loaned you $$98750$$ USD. If you wanted the loan repayment plus interest to be $$100000$$, then they should have loaned you $$\frac{100}{101.25} \cdot 100000 = 98765.43$$