# calculus

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what normal annual interst rate has an effective annual yield of 7.8% under continuous compounding?

• calculus -

We calculate the amount after t=1 year at rate r under continuous compounding, and equate it to 1.078:

1.078=1*ert
take natural log on both sides:
ln(1.078)=r*1
r=ln(1.078)
=0.07511
or 7.511% p.a.

• calculus -

thanks

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