Need math help with finite mathematics "True or False" #3

Mathematics
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True or false. If interest is compounded annually, then the effective rate of interest is the same as the nominal rate of interest.

* If statement is false, make the statement true.

Nov 10th, 2015

Thank you for the opportunity to help you with your question!

The compound interest formula is  A = P*(1 + r/k)^(kt)   where k is the number of compounding periods in a year.  because it compounds annually  k =1  so   the formula becomes  A = P*(1 + r)^t

where t is in years and r is the annual percentage rate.

But nominal interest on an investment of P dollars looks like total = P +  P*r*t  here  the expression is not exponential compared to A = P*(1 + r)^t  where t is in the exponent position.

For example  say the initial amount of money is P = $200 with an annual interest rate r = 5%

after 2 years  If we compounded annually our total amount = 200*(1 + 0.05)^2 =  $220.50

If we earn Nominal Interest our total amount = 200 + 200*0.05*2 = $220

There is your difference.  The original statement is false.  The effective interest rate is not the same as the nominal interest rate if interest were compounded annually.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 10th, 2015

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Nov 10th, 2015
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Nov 10th, 2015
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