Question

You've been offered an investment opportunity that will pay you $10,000 in three years. It is somewhat risky, so you would only take on this investment if you earned a 20% annual return with annual compounding. What is the most that you would pay for this investment today?

1. are you trying to find a PV or FV?
2. show your calculations using the formula
3. show your calculations using the keystrokes for your financial calculator (state which financial calculator you are using)
4. what would your answer be if you required monthly compounding and why is there a difference?

Answer 1

1). TI BA II Plus calculator:

ON --> 2nd --> CLR TVM --> CE|C (for clearing memory and screen)

Enter "-10,000" ---> Press FV

Enter "3" --> Press N (for number of years)

Enter "20%" --> Press I/Y (for annual return)

Press CPT --> PV (for calculating PV)

PV = 5,787.04 (You should not pay more than this for the investment.)

2). PV with monthly compounding:

Steps remain the same as above, except the values become

FV = -10,000; N = 36 ( monthly compounding so 3*12 = 36); I/Y = 1.6667% (calculated as 20%/12 = 1.6667%), CPT PV.

PV = 5,515.32

3). The present values differ in both cases because the number of compoundings during the term is different for both. As a result, the present value with lower frequency of compounding is more than the present value with higher frequency of compounding.