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The simplest approach would probably be to consider a bond that pays coupon continuously. This can be justified as a useful approximation for very frequent (ex. daily) coupon payments, and would allow you to use an integral instead of a summation. The value of such a bond would be: $NPV = \int_0^T \frac{100c}{(1+IRR)^t} \text{d}t + \frac{100}{(1+IRR)^T}$

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