How to solve this annuity question
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How to solve this annuity question

[From: ] [author: ] [Date: 12-06-01] [Hit: ]
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Suppose that an annuity will provide for 20 annual payments of 1280 dollars, with the first payment coming 8 years from now. If the nominal rate of interest is 10 percent convertible monthly, what is the present value of the annuity?

>>Please explain your answer. Thank you!!

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0 ......... 8 ------ 9 ............... 19 ----- 20
to discount to present value, it is best to find the discount factor for one year, which will be D = (1+0.1/12)^-12 =.90521243

PV = 1280(D^8 + D^9 + ...... +D^26 + D^27)
= 1280D^8(1 + D + ...... + D^18 + D^19)
= 1280D^8(1-D^20)/(1-D) .................... (sum of G.P.)

plugging in, PV = $5257 (nearest dollar)
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