(PLEASE SHOW ALL WORK AND VALUES) (PLEASE SHOW ALL WORK AND VALUES) 45) You curr

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(PLEASE SHOW ALL WORK AND VALUES)

(PLEASE SHOW ALL WORK AND VALUES)

45) You currently have $67,000 in an interest-earning account. From this account, you wish to make twenty year-end payments of S5,000 each. What annual rate of return must you make on this account to meet your objective? a) 4.16% b) 5.03% c) 6.42% d) 7.32% 46) After winning the lottery, you state that you are indifferent between receiving twenty S500,000 end of the year payments (first payment one year from today) and receiving a lump sum payment of S5,734,961 today. What interest rate are you using in your decision making process such that you are indifferent between the two choices? a) 5% b) 6% c) 7% d) 8%

Explanation / Answer

45.

Current amount = $67,000

Required annual payments = $5,000

Number of annual payments = n = 20

Let the annual rate of return = r

Current amount = Present value of 20 year end payments

Present value of annuity = Annuity amount*{1-(1+r)-n}/r

$67,000 = $5,000*{1-(1+r)-20}/r

Solving above, r = 4.16%

Hence, correct answer is a) 4.16%

46.

Lump sum amount to be received today = $5,734,961

Annual payments = $500,000

Number of annual payments = 20

To be indifferent between the two options, the present value of annual payments need to be equal to the lump sum payment to be received today.

Present value of annuity = Annuity amount*{1-(1+r)-n}/r

$5,734,961 = $500,000*{1-(1+r)-20}/r

Solving above, r = 6%

Hence, correct answer is b) 6%

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