Mary said there is no difference between an 8% annual interest rate compounded quaterly and annual interest rate. Explain to mary why she is wrong. with examples

Expert Answers

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If an 8% annual interest rate is compounded quarterly, the rate per quarter is 8/4 = 2%.

So an amount $100, in a year would become $100*( 1 + .02)^4

=> $100* 1.02^4

=> $100* 1.0824

=> $108.24

If the compounding is done annually the amount would increase by 8% or become $100*(1 + .08)

=> $108.

So, there is a difference of 24 cents in the two cases.

Even if we take the notional annual interest rate to be the same, as the period of compounding decreases (3 months instead of 12 months), the amount compounded increases after a year.

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