
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
= 12000 * [(1 - (1 / (1 + .12)^10)) / .12]
= 12000 * [(1 - (1 / 3.10584820834421)) / .12]
= 12000 * [(1 - 0.321973236590696) / .12)]
= 12000 * 5.65022302841087
= 67802.68
or the simpler way is to use the new present value of an annuity function in a spreadsheet with 12000 as the payment, .12 as the interest rate, and 10 as the term.
If they’re paying the first $ 12000 up front, then 9 more payments over the next 9 years, do the same estimate as above using 9 as the “n”, which gives $ 63939.00, plus the initial $ 12,000 for a total of $ 75939.00
NPV=P/(1+i)^n
e.g.
- Yr 0 $ 12000 = $ 12000 NPV @ 12% interest
- Yr 1 $ 12000 = $ 10714 NPV @ 12% interest
- Yr 2 $ 12000 = $ 9566 NPV @ 12% interest
.
- Yr 9 $ 12000 = $ 4327 NPV @ 12% interest
so, the lottery need a total of $ 63939 investment to match $ 12000 yearly payment. I used this to calculate my stock intrinsic value anyway.

















