A person wants to borrow $100,000 to buy a house. He intends to pay back a fixed sum of $C at the end of each year, so that after 25 years he has completely paid off the debt. Assuming a steady interest rate of 4% per year, explain why:

$\displaystyle 100,000 = C(\frac{1}{1.04} + \frac{1}{1.04^2} + \frac{1}{1.04^3} + ... + \frac{1}{1.04^{25}})$

I don't understand how is that even possible. If there's an interest rate of 4% per year, it should be a exponential growth, such that:

Total payable sum = $$\displaystyle 100,000 * 1.04^{25}$ ~= 266584$ .. Dividing that by 25 gives $10,663 but that obviously isn't the answer.

I have tried many other ways but I don't seem to get it