# Discounting and continuous compounding

I know there is a relationship between discounting by (1+Rf)T and e-R(f)xT but for the life of me can’t figure it out.

Any of you math wizards able to clarify this relationship for me so I can understand it?

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Tez4715 wrote:
I know there is a relationship between discounting by (1+Rf)T and e-R(f)xT but for the life of me can’t figure it out.

Any of you math wizards able to clarify this relationship for me so I can understand it?

First, multiplying by eR(f)T is the same as dividing by eR(f)T, just as discounting by (1 + Rf)T is accomplished by dividing by (1 + Rf)T.

Second, if R(f) is the continuously compounded rate, and Rf is the annual effective rate, then

eR(f) = 1 + Rf

Finally,

eR(f)T = [eR(f)]T

so,

eR(f)T = [eR(f)]T = (1 + Rf)T

Therefore, multiplying by eR(f)T is the same as dividing by eR(f)T, which is the same as dividing by (1 + Rf)T.

Voilà!

Simplify the complicated side; don't complify the simplicated side.

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Brilliant, thank you Sir. That makes interpreting the BSM much easier!

Pushing will get a person almost anywhere, except through a door marked “pull”

You’re quite welcome.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/