Suppose you win the lottery, and you will be paid $10 000 000 over 10 years, in other words, $1 000 000 per year for 10 years. If the money is invested at 8% interest, compounded annually. How much money does the lottery company have to have saved up in order to pay you your $1 000 000 each year?
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Lottery savings
- Thread starter haister
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You ask:Suppose you win the lottery, and you will be paid $10 000 000 over 10 years, in other words, $1 000 000 per year for 10 years. If the money is invested at 8% interest, compounded annually. How much money does the lottery company have to have saved up in order to pay you your $1 000 000 each year?
How much money does the lottery company have to have saved up
What is the interest rate for savings?
The solution will follow a GP:
Year 1 = 1000000
Year 2 = 1000000/1.08
Year 3 = 1000000/1.08^2
Year 4 = 1000000/1.08^3
.
.
.
.
Year 9 = 1000000/1.08^8
Year 10 = 1000000/1.08^9
Lottery will need to have saved up = 1000000(1+1/1.08+1/1.08^2+1/1.08^3+.....+1/1.08^9) = $7250000 (3 s.f)
It is an interesting, but typical problem which involves a straight-up first payment, then the same fixed amount with subsequent years. This can also be simplify to this G.P. formula:
S = k (1-(1/1+r)^n)/1-(1/1+r)
Where k=required fixed amount payment each year, r=interest rates (as a decimal), n number of years.
Year 1 = 1000000
Year 2 = 1000000/1.08
Year 3 = 1000000/1.08^2
Year 4 = 1000000/1.08^3
.
.
.
.
Year 9 = 1000000/1.08^8
Year 10 = 1000000/1.08^9
Lottery will need to have saved up = 1000000(1+1/1.08+1/1.08^2+1/1.08^3+.....+1/1.08^9) = $7250000 (3 s.f)
It is an interesting, but typical problem which involves a straight-up first payment, then the same fixed amount with subsequent years. This can also be simplify to this G.P. formula:
S = k (1-(1/1+r)^n)/1-(1/1+r)
Where k=required fixed amount payment each year, r=interest rates (as a decimal), n number of years.