Why is there interest in Perpetuity?

That's like asking why there is water in rain drops. If there wouldn't any interest then it wouldn't be a perpetuity. In a perpetuity, you are making regular withdrawals but no more than what the investment is earning in interest so therefore it's a continual source of income as the original investment is never drawn upon. It's only the same amount of money because your regular withdrawals equal the interest earned.

If you were to be making the annuity payments to someone else and wanted to just put all the money necessary to make those payments into a savings account at that interest rate then C/(1+r) is what you need to save now at that interest rate to make the first year's payment, C/(1+r)^2 is what you need to save now to make the second, etc. Because it's a geometric sequence and 1/(1+r) is less than 1, the summation of what you have to save for all payments converges to a finite value.