The question states - Party A will receive $104,000,000 in one year from Party B because of their contract. It has now been 9 months. Calculate the present value of this future receipt i.e 3 months before you get the $104,000,000. The interest rate is 4%

The basic manual calculation is $104,000,000 / (1.04^{(3/12)}) = $102,985,244.50

On the TI BA 2 Plus Pro, the keystrokes that I’m putting are:

N = 3

I/Y = (4/12) = 0.333333333

PMT = 0

FV = $104,000,000

Compute PV and the answer is -$102,966,895.

The difference between manual method and calculator is $18,349.49 !!!

I know the manual method should give the right answer.

The actual question was the one party went long a one year 100 million forward contract. The risk free rate is 4% and hence the party expects to receive 104 million one year from now. 9 months later the spot price of the underlying is 101.5. I’m trying to calculate the credit risk for the contract.

So basically what I need to do is 101.5 - (PV of 104 million to be received 3 months from now).

For that I needed to calculate PV of 104 million and was getting 2 different answers with manual method i.e 104 million / (1.04^{(3/12)}) and key strokes on calculator.

I can’t believe that getting a simple TVM result is sooooo tedious on a financial calculator!

If you have a better way to calculate the PV number, please let me know how to go about it.

Do TVM keys really do simple interest and not compound interest?

From my understanding TMV keys do simple interest, if you want to compound interest you got to do the calculations with the # of periods, like you did above, 4/12 gives the compound interest.

That tells you that 4% is an effective annual rate: you’re quoted 4% per year and at the end of one year you get _ exactly _ 4%.

Um . . . no.

Read what you and I wrote above.

You wrote that you thought that they did only compound interest.

I agreed.

That’s the problem: if you’re given an effective annual rate of 4%, then dividing it by 12 does not give you an effective monthly rate, so you cannot compound 4% / 12 = ⅓%.

To get the effective rate for 3 months you can:

Get the monthly (effective, compound) rate (1.04^{1/12} − 1 = 0.3274%) and use n = 3

Get the quarterly (effective, compound) rate (1.04^{1/4} − 1 = 0.9853%) and use n = 1

If you were given a nominal (compounded monthly) annual rate of 4%, then dividing it by 12 would give you an effective monthly rate of ⅓%, but they’d specify that the annual rate is nominal and that it’s compounded monthly.

Interestingly, when I tried it this way (a brilliant idea, by the way, breadmaker) on my (old) HP 12C, it gave the wrong answer. Apparently it doesn’t like n to be fractional (i.e., not a whole number)