Present Value of a Single Amount Problems and Solutions

 

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

Solution: 

1,000 / (1 + 0.12) 2

Answer: $797.19

 

(b) 12% per year discounted semi-annually

Solution: 

1,000 / (1 + 0.12/2) 2*2

Answer: $792.09

(c) 12% per year discounted daily

Solution: 

1,000 / (1 + 0.12/365) 2*365

Answer: $786.66

 

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?

 

Solution: 

1,000,000 / (1 + 0.16) 60

Answer: $135.68

 

Problem 3: Using present value formula

$7,000 for 10 years from now at 7% is worth how much today?

 

Solution: 

7,000 / (1 + 0.07) 10

Answer: $3,558.45

 

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?

 

Solution: 

84,253 (PVIF 11%, 5)
84,253 (0.5935)

Answer: $50,004.16 

>> Download Present Value Tables.



 

Problem 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?

Solution: 

3,060 / (1 + 0.12) 3

Answer: $2,178.05

 

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?

 

Solution: 

2,000 / (1 + 0.08) 3

Answer: $1,587.66

 

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?

 

Solution: 

14,000 / (1 + 0.17) 2

Answer: $10,227.19

 

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?

Solution: 

(80,000/50,000) (1/10) – 1

Answer: 4.81%

 

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?

 

Solution: 

10,000 / (1 + 0.06 / 4) 5 * 4

Answer: $7,424.46

 

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?

 

Solution: 

15,000 / (1 + 0.12/12) 1*12

Answer: $13,311.74

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