Thursday, July 2, 2009

Answer to Nominal Profits

Your savings account pays 12% annually continuously compounded but pays out the interest to you in quarterly installments. How much interest will be paid on your 1,000-dollar deposit each quarter?

e^R=(1+r/m)^m, where e^.12=(1+r/4)^4. We take the natural log of each side
.12=4 ln(1+r/4)then we move the 4 to the left side so that .03=ln(1+r/4) Then we raise both sides by e so that e^.03 = (1 +r/4) so that 4(e^.03 -1)= r and therefore r=12.18%. For future reference we can just note that r=m(e^(R/m)-1)

To fully answer the question, we must take the 1000*(.1218/4)= 30.46 which is the dollar amount paid out per quarter on the account.

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