You’ve just won the lottery which promises to pay you $5,000 per month for the next...

You’ve just won the lottery which promises to pay you $5,000 per month for the next 30 years, starting in one month. The lottery company is require to buy US Treasury securities to guarantee that it can meet its obligation to you. If Treasury securities earned 5% APR compounded monthly, how much would the lottery company have to invest today to cover its obligation?

Expert Solution

	Investment today	P×[1-(1÷(1+r)^n)]÷r

	Here,

1	Interest rate per annum	5.00%
2	Number of years	30
3	Number of compoundings per per annum	12
4 = 1÷3	Interest rate per period ( r)	0.42%
5 = 2×3	Number of periods (n)	360
	Payment per period (P)	$ 5,000

	Investment today	$ 931,408
		5000*[1-(1/(1+0.42%)^360]/0.42%

jeff jeffy answered 1 year ago

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