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# 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

(b) 12% per year discounted semi-annually

### Solution:

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

(c) 12% per year discounted daily

### Solution:

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?

### Solution:

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?

### Solution:

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?

### Solution:

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

## 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

## 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

## 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

## 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

## 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

## 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

## References

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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