Question

Answer each of the following independent questions. Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: (1) $64,000 cash immediately, (2) $20,000 cash immediately and a six-period annuity of $8,000 beginning one year from today, or (3) a six-period annuity of $13,000 beginning one year from today. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) 1. Assuming an interest rate of 6%, determine the present value for the above options. Which option should Alex choose? 2. The Weimer Corporation wants to accumulate a sum of money to repay certain debts due on December 31, 2030. Weimer will make annual deposits of $100,000 into a special bank account at the end of each of 10 years beginning December 31, 2021. Assuming that the bank account pays 7% interest compounded annually, what will be the fund balance after the last payment is made on December 31, 2030?

Answer 1

1. Option 1
2. $1,381,645

Step-by-step explanation:

1. Alex needs to pick the option that offers the highest present value.

Option 1 present value = $64,000

Option 2:

Mix of lump-sum and annuity:

Present value of annuity = Annity * Present value interest factor of annuity, 6%, 6 periods

= 8,000 * 4.9173

= $‭39,338.4‬0

Present value of option B = 20,000 + ‭39,338.4‬0

= $59,338.40

Option 3:

Present value of annuity = Annity * Present value interest factor of annuity, 6%, 6 periods

= 13,000 * 4.9173

= $‭63,924.9‬0

Alex should choose option 1 as it has the largest present value.

2.As this concerns a future amount, the future value of an annuity is used.

Future value of Annuity = Annuity * (( 1 + rate)^n - 1 )/ r

= 100,000 * ((1 + 7%)¹⁰ - 1) / 7%

= 100,000 * 13.8164479612795

= $1,381,644.79

= $1,381,645