Finance Question...Please help me. I\'m not sure how to do the calculations or w

Question

Finance Question...Please help me. I'm not sure how to do the calculations or which formulas to use. May you please explain to me step by step?

Assume that you just won $30 million in the Florida lottery, and hence the state will pay you 20 annual payments of $1.85 million each beginning immediately. If the rate of return on securities of similar risk to the lottery earnings (e.g., the rate on 20-year U.S. Treasury bonds) is 6 percent, what is the present value of your winnings?

While Anderson Brooke was a student at UNC-CH, he borrowed $20,000 in student loans at an annual rate of 8 percent. If Anderson repays $2,000 per year, how long to the nearest year, will it take him to repay the loan?

Explanation / Answer

Present value of winnings = P+P×[1-(1÷(1+r))^(n-1)]÷r

r is interest rate

P is payment per period

n is number of payments

= $1,850,000+$1,850,000×[1-(1÷(1+6%))^(20-1)]÷6%

= $22,492,515.51

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