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BA II Plus: Continuous Compounding Step by Step

Use LN and e^x on the BA II Plus for continuously compounded returns and discounting.

TL;DR

Continuous compounding uses natural logs and exponentials. Use LN for continuously compounded returns and e^x for continuous discounting or accumulation.

Formula Reference

Continuously compounded return

r_c = ln(FV / PV) / t

Annualize by dividing by time in years.

Continuous discounting

PV = FV x e^(-rt)

Common in derivatives and fixed income.

BA II Plus Keystrokes

Compute FV / PV
Press LN
Divide by t for the continuous rate
For discounting, compute -r x t
Press 2nd e^x
Multiply by FV

Worked Example

PV = 100, FV = 110, t = 1.
Continuously compounded return = ln(110 / 100) = 9.53 percent.
Use LN after computing the value ratio.

Common Mistakes

Using simple return when continuous return is requested.
Forgetting the negative sign in continuous discounting.
Using log base 10 instead of natural log.

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CFA Level I Derivatives Formula Sheet - Public formula sheet for forwards, futures, options, put-call parity, and Black-Scholes inputs.
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