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!!
>>Please explain your answer. Thank you!!
-
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)
------------------- -------------------------------
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)
------------------- -------------------------------