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An interest rate call option and put option based on a 90day underlying rate both have an exercise rate of 7.5% and expire in 180

An interest rate call option and put option based on a 90day underlying rate both have an exercise rate of 7.5% and expire in 180 days. The forward rate is 7.75% and the volatility is 0.045. The continuously compounded risk-free rate is 5%. Calculate the price of the interest rate put options using the Black model (round to 8 decimal places).

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