Calculating Present value (PV) using BA II Plus calculator

CFA Level I
#1

A firm is interested in purchasing a $100 US Treasury bill. Here are the details….

Due date of payment- 180 days from investment day

Annual interest = 6%

I need to find the present value

I calculated Present value in two ways using BA II Plus calculator as under:

1st way

N=1

I/Y = 6 x (180 / 360) = 3

FV = 100

CPT PV = -97.08

2nd way

N = 1 x (180 / 360) = 0.50

I/ Y = 6

FV = 100

CPT PV = - 97.12

I want to know:

  • Which of the Present Value is correct

  • Why the two calculations are showing different present values?

  • When should one calculate present value the 1st way and when should one calculate present value the second way

#2

Under method 1, you are assuming semi-annual compounding (0.06 / 2 = 0.03), but under Method 2, you are assuming annual compounding (1.06^0.5 - 1 = 0.02956).

Any question you get on the exam should specify the compounding frequency.

#3

Thank you. This helps

Please let me know the formula derivation for (1.06^0.5 - 1 = 0.02956)

#4

Effective interest rate computed by you is 3 and nominal interest rate computed is 2.956 (using formula)

I tried to get nominal interest rate using BA II Plus calculator but am getting a different answer

2nd and ICONV

EFF = 3 ENTER
C / Y =2 ENTER
NOM = CPT = 2.977

Nominal rate computed using BA II Plus is slightly different from manually calculated number using formula. What could be the reason for this ?

#5

If we assume 6% compounded semi-annually, then the effective rate for the 6 month period is 3%. 2.977% is the nominal rate that would apply if you split that 6 month period into two 3 month periods. [ (1+0.02977/2)^2 = 1.02999 ]

2.956% is the rate I would credit if compounding were annual in order to recognize 6 months of interest. [(1+0.02956)^2 = 1.05999]

Any nominal interest rate r has to meet the following relationship:

(1 + r/m)^m = 1 + effective rate where m is the number of compoundings within the period assumed by the effective rate. You have likely seen this formula using an annual period for the effective rate with m compoundings per year, with typical m of 2, 4, 12, 365, all the way to continuous.

#6

Thanks again.

With BA II plus calculator, how to convert 3% (effective interest) to 2.956% (Nominal interest) using ICONV function button or in some other way (other than using the formula) ?