In 2019 Shell PLC issued bonds for which the holder received no interest but at maturity received the face value of the bond, £1000, (this is the amount lent by the bond holder to Shell PLC) plus an additional amount, A, which depended on the price of oil at the bond's maturity. This additional amount was set to be 170 times the excess, if any, of the price of a barrel of oil over £25 sub ject to the con dition that the addition al amount, A, could not exceed £2550. (a) Find a formula for A in terms of S (t), the price of a barrel of oil (in dollars per barrel) at the bond's maturity date T.

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