Download Which is worth more: $1,000 now or $2,000 in 12 yrs @ 6%

Time Value of Money Problems
1. Which is worth more: $1,000 now or $2,000 in 12 yrs @ 6%?
2. Angie needs $500,000 in 10 yrs to fund her retirement. If money is @10%, how much does she need to set
aside in equal amts to reach her goal?
3. An investment costs $6,930 now and in return pays $2,000/yr for 4 years, what rate of return is it generating?
4. You want to buy a house for $50,000 and put 10% down and mortgage the rest over 25 years @ 8%. What
are the annual payments?
Monthly payments?
5. You are offered two different cash flows from two different investments, A and B. Which would you choose
and why? Assume you can invest at a rate of 9%.
YR
1
2
3
4
5
A
10,000
10,000
10,000
10,000
10,000
B
8,000
9,000
10,000
11,000
12,000
6. If you won the Publisher’s Clearing House $10 million prize (payable as 30 pmts of $250,000 and $2.5m in
yr. 30) and could invest the money at 8%, would you accept an offer of $3.5 million payable today?
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Perpetuity
7. How much interest will $1 million pay out each year at 6%?
Annuity Due
8. What is the future value of $100 invested each year for 5 years at 8% starting today?
9. What is the present value of #8?
10. If you invested $4,000/yr for 40 years in an IRA, what is the difference between investing at the end of the
year as compared to the beginning? (evaluate the FV) Assume 10%
Effective rate –
11. 8% compounded semi-annually is what Effective Annual Rate?
*APR – the annualized rate using simple interest. 1%/month = 12% APR
Nominal rate =
12. Which pays more: 7¼ % or 7% compounded quarterly?
13. What would $1,000 at 9% be worth in 10 years? What if compounded semi-annually?
14. If sales for a company grew from $10 million to $20 million in 5 years, what would be the compound
annual growth rate (CAGR)?
15. You desire $70,000/yr. in retirement for 20 yrs. (65-85). You’re 25 now. How much do you need to save
each year for the next 40 years to reach your goal? Assume 10%
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16. Assuming inflation averages 3%, what is a $70,000 job in 40 years equivalent to today?
17. You have just won the lottery of $110 million. If you can make a 10% return do you take the lump sum
today of $59 million or 25 payments of $4.4/yr for 25 years (110m)? At what point do you change your mind?
18. Estimate the future value of $100 in 48 years @ 6%? (Use “Rule of 72”)
19. A car dealer is selling a new Ford truck for $20,000 and offering 7% financing for 5 years. He is planning
to run a zero-interest sale during which a person would finance the truck over 5 years at 0% interest. How much
would he need to charge during the sale in order to get the same annual payment (as without the sale)?
20. Under the terms of a liability lawsuit settlement, David Brin will be paid $10,000 today, $1,000 at the end of
each year for the next 10 years and $2,000 a year for 5 years after that. If David’s opportunity cost of money is
7%, what is the value of this settlement today?
21. How much interest is paid on a loan of 5 $100 annual payments at 8%?
22. How much interest is paid on a $200,000 mortgage over 30 years at 7%? (assume annual payments)
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23. IBM has a project which has the cash flows listed below. What cash flow will the project have to generate in
the fourth year in order for the project to have a 15% rate of return?
Year Cash Flow
0 -500
1 150
2 100
3 60
4 ?
24. David Bach talks about the “Latte Factor” in his book The Automatic Millionaire. He is referring to saving
$5 a day by abstaining from drinking a Starbuck’s coffee. If you invested this money over 40 years at 10%, how
much would you save? What if your 401k matched 50% of this investment?
25. In 1889, Van Gogh’s painting, “Sunflowers”, sold for $125. In 1987 it sold for $36 million. Had the
painting been in your family, how much would your average annually compounded rate of return have been?
n=98
26. The average wedding cost around $20,000. If you and your fiancé had a small wedding at a cost of $5,000
and invested the rest for retirement in 40 years at 10%, how much would you have accumulated?
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