HI

@Tim_Rogers The exp(rt) compounds forward over T years with continuous compounding. For example, $10.00 today (i.e., present value) grows at 7.0% per annum with continuous compounding over five (5) years to a

*future value *of 10*exp(0.07*5) = $14.19. This is just the continuous analog to, say, semi-annual compounding which would produce a future value of 10*(1 + 0.07/2)^(5*2) = $14.11. If we take F0 = S0*exp(rt) and divide both sides by exp(rt), then we have solved for the current spot (i.e., present value) as a function of the future price: S0 = F0/exp(rt) = F0*exp(-rt) because 1/a^b = a^(-b) and

**1/exp(a) = exp(-a)**. So if we want the present value of $10.00 to be received in five years, discounted at 7.0% per annum with continuous compounding, then the PV = 10/exp(0.07*5) = 10*exp(-0.07*5) = $7.05; and we could test it by compounding forward: $7.05*exp(0.07*5) = 10.00. And this is the continuous analog to, say, semi-annual discounting which would instead give us a PV = 10/(1+0.07/2)^(5*2) = 10*(1+0.07/2)^(-5*2) = 7.09. I hope that's helpful,

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