Answer:
An annuity that pays $1,000 at the beginning of each year
PTM of the annuity selling for 2,541.15 $ 437.50
Present value of the Jackpot: $62,063,701
Explanation:
Because is at the beginning, the 1,000 will be generating interest right away.
So even the 500 at the beginning will have a slightly higher rate, it cwon't compensate the 1,000 upfront.
Calculate the annual payment:
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = PTM\\[/tex]
PV $ 2,514.15
time 8 years
rate 8% = 0.08
[tex]2514.15 \times \frac{1-(1+0.08)^{-8} }{0.08} = PTM\\[/tex]
PTM $ 437.50
jackpot present value of an annuity-due (payment at beginning)
[tex]PTM \times \frac{1-(1+r)^{-time} }{rate} (1+r)= PV\\[/tex]
PTM $10,000,000
time 8 years
discount rate 0.08
[tex]10000000 \times \frac{1-(1+0.08)^{-8} }{0.08} (1+0.08)= PV\\[/tex]
PV $62,063,700.5922
