Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: (1) $64,000 cash immediately, (2) $21,000 cash immediately and a six-period annuity of $7,700 beginning one year from today, or (3) a six-period annuity of $13,300 beginning one year from today.
1. Assuming an interest rate of 7%, 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, 2027.
Weimer will make annual deposits of $115,000 into a special bank
account at the end of each of 10 years beginning December 31, 2018.
Assuming that the bank account pays 8% interest compounded
annually, what will be the fund balance after the last payment is
made on December 31, 2027?
Assuming an interest rate of 7%, determine the present value for the above options. Which option should Alex choose? (Round your final answers to nearest whole dollar amount.)
|
|
Answer:
1) | Annuity Payment | PV Annuity @7% | Immediate Cash | PV Option | ||
Option 1 | $0 | 1 | + | $64,000 | = | $64,000 |
Option 2 | $7,700 | 4.7665 | + | $21,000 | = | $57,702 |
Option 3 | $13,300 | 4.7665 | + | $0 | = | $63,394 |
2) Alex can choose Immediate cash option as $64,000 (i.e Option 1) |
3) Weimer Fund balance end of 2027 is given below | |||||
n=10 Years | |||||
i=8% | |||||
FV={A*(1+i)^n-1}/i | |||||
so {115,000*(1+.08)^10-1}/.08 | |||||
so 115,000*(2.1589-1)/.08 | |||||
so 115,000*14.4863 | |||||
Future value | 16,65,925 | ||||
So Total Fund Balance end of 2027 is $16,65,925 |
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