How to price this option using the Black Scholes model?

I have a question regarding regular option pricing.

In the standard Black-Scholes model, with interest r and volatility $\sigma$, I have to eetermine the arbitrage free price at time $t$ of an option which at $T>t$ pays the holder the amount of 100 USD dollar if the stock price is between 50 and 100 USD.

I.e. an option with payoff function:

$$\phi(S) = 100 ~ \text{if} ~ 50<S_T<100 ~ \text{else} ~ 0$$

A thorough walk through in how to calculate this price would be highly appreciated.

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