An ordinary annuity selling at $13,044.14 today promises to make equal payments

Question

An ordinary annuity selling at $13,044.14 today promises to make equal payments at the end of each year for the next six years (N). If the annuity's appropriate interest rate (I) remains at 1 1.00% during this time, the annual annuity payment (PMT) will be You just won the lottery. Congratulationsl The jackpot is $60,000,000, paid in six equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won assuming annual interest rate of 11.00%. MAC 310,0,108 2004-2016 Apla. All ights reserved 3 3341 Orade It Now 2013 Cengege Learning escept as noted. All rights reserved

Explanation / Answer

1.

Sale value of ordinary annuity = Present value of annual annuity payment

Sale value of ordinary annuity = $13,044.14

Interest rate = r = 11%

Number of annuity payments = n = 6

Present value of ordinary annuity = Annuity payments*{1-(1+r)-n}/r

$13,044.14 = Annuity payment*(1-1.11-6)/0.11

$13,044.14 = Annuity payment * 4.23054

Annuity payment = $13,044.14/4.23054 = $3,083.33

2.

The six beginning of year lottery payments starting from today shall form an annuity due.

Annual lottery payment = $60,000,000/6 = $10,000,000

Annual interest rate = r = 11% = 0.11

Number of annual payments = n = 6

Present value of annuity due = Annuity payment + Annuity payments*{1-(1+r)-(n-1)}/r

Real value of lottery = $10,000,000 + $10,000,000*(1-1.11-5)/0.11 = $46,958,970.18

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