Present Value of a Single Amount Problems and Solutions
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Problem 1: Present value intra-year discounting
What is the present value of $1,000 received in two years if the interest rate is?
(a) 12% per year discounted annually
1,000 / (1 + 0.12) 2
(b) 12% per year discounted semi-annually
1,000 / (1 + 0.12/2) 2*2
(c) 12% per year discounted daily
1,000 / (1 + 0.12/365) 2*365
Problem 2: Present value of a single amount
You have just won a $1 million lottery. This new lottery, however, will pay out the award 60 years from today. What is the present value of your award based on a 16% p.a. interest rate?
1,000,000 / (1 + 0.16) 60
Problem 3: Using present value formula
$7,000 for 10 years from now at 7% is worth how much today?
7,000 / (1 + 0.07) 10
Problem 4: Present value table
What is the present value of $84,253 to be received or paid in 5 years discounted at 11% by table and factor formula?
84,253 (PVIF 11%, 5)
Mr. Nadeem owes a total of $3,060 which includes 12% interest for the three years he borrowed the money. How much did he originally borrow?
3,060 / (1 + 0.12) 3
Problem 6: Present value annual discounting
If we want $2,000 three years from now and the compounded interest rate is 8%, how much should we invest today?
2,000 / (1 + 0.08) 3
Problem 7: Present value of a single amount
What is the present value of an offer of $14,000 two years from now if the opportunity cost of capital (discount rate) is 17% per year discounted annually?
14,000 / (1 + 0.17) 2
Problem 8: Finding interest rate
If you invested $50,000 at one point in time and received back $80,000 ten years later, what annual interest (or growth) rate (compounded annually) would you have obtained?
(80,000/50,000) (1/10) – 1
Problem 9: Intra-year discounting
How much would you have to deposit today to have $10,000 in five years at 6% interest discounted quarterly?
10,000 / (1 + 0.06 / 4) 5 * 4
Problem 10: Present value discounted monthly
What is the present value of an offer of $15,000 one year from now if the opportunity cost of capital (discount rate) is 12% per year nominal annual rate compounded monthly?
15,000 / (1 + 0.12/12) 1*12
Financial Management: Theory and Practice, Dr Eugene F Brigham & C Micheal Ehrhardt
Fundamentals of Financial Management: Concise Edition, Brigham Houston
The Economist Guide to Financial Management, John Tennet
Financial Management: Core Concepts, Raymond M Brooks
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