Valuation of Interest rate futures

Could someone please explain what these two sentences mean?

The 3month fwd on 1 year MRR = 5%
Future = 100 - 5 = 95
At expiry
Interest rate moves to 7%
Future = 100 - 7 = 93
The relationship is linear.
At expiry
Interest rate moves to 9%
Future = 100 - 9 = 91

The relationship between interest rates and price of future linear.

Assume Notional principal = $1m
Payoff on forward is different.
At 7%
(MRR diference) x time adjustment x NP / disocunted
(7 -5) x 1 / ( 1.07) = 1.86
At 9%
(MRR diference) x time adjustment x NP / disocunted
(9 -5) x 1 / ( 1.09) = 3.67

Due to discounting element the relatinship between interest rates and forward value is NOT LINEAR it is convex.

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Thanks @MikeyF . The examples make it clear. But why does one have discounting whereas the other does not?

Didn’t get you :smiling_face_with_tear:

Sorry.

FRA are OTC no margin, early payment =to reduce credit risk and hence disocunting.

STIR futures with margin and no credit risk. Discounting payoff to reduce credit risk is irrelavant.