please answer all three You have just won a share of the lottery and have the op

Question

please answer all three

You have just won a share of the lottery and have the option to receive one of the following payouts: $500,000 cash immediately. $200,000 cash immediately and four equal payments of $75,000 a year, first payment made at the end of the first year and each year end for four years ten annual payments of $55,000, first payment made at the end of the first year Assuming an interest rate of 3%, which option would be financially the best payout? Show work. You want to buy a new car in 10 years, but you want to be able to pay cash. The car you want to buy will cost $28,654 in 10 years. You have $16,000 to invest today. What interest rate would you have to earn in order to have the money you need in 10 years? You have borrowed money from a friend in order to buy books for the next semester and agreed to pay back the $2,000 in 5 years. You have agreed to pay $ 150 interest each year for the next 5 years. Assuming an interest rate of 8%, what is the amount you borrowed?

Explanation / Answer

present worth in the three given case

1) $ 500,000

2) $ 200,000 + A [ (1+i)^n - 1]/{(i (1+i)^n]

200000 + 75000 [(1+0.03)^4 - 1/ 0.03*1.03^4] = $ 478782.38

3) 55000 [(1+0.03)^9 -1/0.03 *1.03^9] = $ 428236

so 1st one is a better option

B) future worth = P (1+i)^n

28654 = 16000 ( 1+i)^10

i = 6%

C) P = 2000/ 1.08 ^ 5 = $ 1361.17

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