Note 1: In order to receive full credit a cash flow diagram is required for ever

Question

Note 1: In order to receive full credit a cash flow diagram is required for every problem Note 2: All calculations, cash flow diagrams and final answers should be written on a separate sheet of paper with your name written in the upper right hand corner of every page. 1) The state lottery has given you the terrific news that you have just won the $3M jackpot and that you now have to choose whether you will receive a single payment of $3M (which you can put into the bank) or you will eceive an annuity of $120,000 per year for the next 30 years. The available bank interest rate is 6%. Assuming that you don't actually spend any of this money which choice will leave you in a better financial position in 30 years? Explain your answer. (Note: Be sure to thank your ENGR 140 instructor for preparing you to make this decision!) 2) Joe Hornet has $10,000 in his savings account from an inheritance 10 years ago. If the savings account pays interest annually at a rate of 5%, how much was initially deposited in his savings account 10 years ago? Assume compound interest. 3) If you put any amount of money in the bank at 7% compounded interest how long will it take to triple your money? How long will it take to triple your money if a simple interest calculation is used.

Explanation / Answer

ANSWER:

1) amount to be recieved in annuity = $120,000

n = 30 years

i = 6%

pw of annuity = amount to be recieved in annuity(p/a,i,n)

pw of annuity = 120,000(p/a,6%,30)

pw of annuity = 120,000 * 13.765

pw of annuity = $1,651,800

since the pw of annuity is less then $3 million dollars , therefore it is better to take $3 million dollars now.

2) future value = $10,000

i = 5%

n = 10 years

pv = fv(p/f,i,n)

pv = 10,000(p/f,5%,10)

pv = 10,000 * 0.6139

pv = $6,139

so the amount deposited 10 years ago was $6,139.

3) a) for compound interest:

let present value = $100

future value = $300 ( since it has to be tripled)

n = ?

i = 7%

fv = pv(f/p,i,n)

300 = 100(f/p,7%,n)

300 / 100 = (f/p,i,n)

3 = (f/p,i,n)

looking in the table of 7% compound interest , the n comes between 16 and 17 years.

n = 16.23 years ( solving further)

b) in simple interest:

a = 300

p = 100

r = 7%

t = ?

a = p * (1 + rt)

300 = 100 * (1 + 7% * t)

300 / 100 = (1 + 0.07t)

3 = 1 + 0.07t

3 - 1 = 0.07t

2 = 0.07t

t = 2 / 0.07

t = 28.57 years

so in simple interest it will take 28.57 years.

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