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FRA - calculating value before maturity

Anyone understand the intuition behind:

When valuing a FRA before maturity of contract, we take the difference between the old FRA price calculated at inception and the new FRA price calculated at Time t. 

I understand the methodology behind calculating this. However, I don’t understand it conceptually. 

Anyone able to provide clarification on what is really going on behind these calculations?

Thanks

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If you can do it correctly but don’t know why, you have intuition.

If you know why, you have understanding.

The value of any derivative – or of any investment, for that matter – is the present value of what you will receive minus the present value of what you will pay.

In the case of an FRA (if you’re receiving the fixed payment), that’s the difference between the original fixed rate and the current (market) fixed rate, discounted back to today.

Simplify the complicated side; don't complify the simplicated side.

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