Each payment or deposit for an annuity due earns one

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Unformatted text preview: ing for compounding that occurs during the year occurs If you want to compare two alternative If investments with different compounding periods you need to compute the EAR and use that for comparison. use 18 Interest Rates: Annual Percentage Rate(APR) This is the annual rate that is quoted by law By definition APR = period rate times the number By of periods per year of Consequently, to get the period rate we rearrange Consequently, the APR equation: the Period rate = APR / number of periods per year You should NEVER divide the effective rate by the You number of periods per year – it will NOT give you the period rate the 19 EAR - Formula EAR =(1+ APR m m ) -1 m = # of compounding periods in a year Remember that the APR is the annual quoted rate! What is the EAR if the APR is 12% Compounded quarterly? .12 4 (1+ 4 ) - EAR = = .1255 = 12.55% 1 20 Computing APRs from EARs If you have an effective rate, how can you compute the APR? Rearrange the EAR equation and you get: and 1 m (1 + EAR) APR = m - 1 What is the APR if the EAR is 12.55% and Interest is compounded quarterly? 1 4 (1 + .1255) APR = 4 APR = 12.00% - 1 Things to Remember about interest rates 21 You ALWAYS need to make sure that the interest You rate and the time period match. rate If you are looking at annual periods, you need an annual rate. If you are looking at monthly periods, you need a monthly rate. If you have an APR based on monthly If compounding, you have to use monthly periods for lump sums, or adjust the interest rate appropriately if you have payments other than monthly monthly Annuities and Perpetuities Defined 22 Annuity – finite series of equal payments that Annuity occur at regular intervals occur If the first payment occurs at the end of the period, it is called an ordinary annuity If the first payment occurs at the beginning of the period, it is called an annuity due Perpetuity – infinite series of equal payments 23 Perpetuity A Perpetuity is an annuity that makes payments Perpetuity forever. forever. Examples Nobel Prize Endowment Scholarship Funds In order to withdraw a constant amount forever, In never withdraw the principal--only the accrued interest. interest. PV = PP i 24 Perpetuity Example: Donna struck it rich as a result of her education at ODU. In order to properly thank the faculty she sets up an endowment to be used for scholarships. Annual costs are approximately $5,000/year. If interest rates are currently 5%, how much must she give to grant one full scholarship per year forever? PV = PV = 5,000 .05 PP i = 100,000...
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