TVM Problem - Calculator input issue

[system]

Hi there

I am slightly confused regarding very simple TVM entry into the BAII Plus calculator. Please refer to the example below:

What is the price of a 10-Year $1000 Face Value bond with a Coupon Rate of 4.0% that pays semi-annually, if the yield is 6.0%?

My calculator entries:

N = 10

I/Y = 6%

P/Y = 2 (Semi-Annual)

C/Y = 2 (Automatically changes when you change P/Y)

PMT = $40

FV = $1000

CPT -> PV = -$1085.3

The computed PV answer is wrong, the answer should be $851.23. I have accounted for the compounding and payment periods being 2 times per year in respects to C/Y & P/Y, so to my understanding it is not necessary for me to then divide the YTM by 2.

Can someone please let me know what I am doing wrong?

[Test_20]

you would need to convert I/Y (3%) and N (5) to semi-annual as well. The calculator on the end mode and entries should be used N, I/Y, PMT, FV and compute for PV.

[breadmaker]

N is the number of payments, not the number of years. You can enter 20 directly, or you can enter 10 2nd N (which will multply 10 by 2) and hit N again to register the 20.

PMT should be the periodic payment of 20 = $1,000 * 4% / 2.

[breadmaker]

@Test\_20

you would need to convert I/Y (3%) and N (5) to semi-annual as well. The calculator on the end mode and entries should be used N, I/Y, PMT, FV and compute for PV.

Going with I=3 means you have to set P/Y=C/Y=1 and N=20. You will get the same PV in the end.

[system]

So then what are the P/Y and C/Y functions useful for then?

Why is it that I can’t just input all the calculations like they are in the problem, and then simply tell the calculator that it is compounded twice a year? Should this not give the same outcome?

Kind regards

[Test_20]

I got it, thanks very much for correcting me:)

[breadmaker]

@R44

So then what are the P/Y and C/Y functions useful for then?

Why is it that I can’t just input all the calculations like they are in the problem, and then simply tell the calculator that it is compounded twice a year? Should this not give the same outcome?

Kind regards

Some candidates like to leave P/Y=C/Y=1 for ALL TVM problems because they don’t want the hassle of changing these values. You can do it this way, but you have to be very careful how you set the interest rate I. This is particularly a problem where the payment frequency and the compounding frequency don’t match. That’s why I tend to go with setting P/Y and C/Y on an annual basis, as set out in the question.

[system]

Some candidates like to leave P/Y=C/Y=1 for ALL TVM problems because they don’t want the hassle of changing these values. You can do it this way, but you have to be very careful how you set the interest rate I. This is particularly a problem where the payment frequency and the compounding frequency don’t match. That’s why I tend to go with setting P/Y and C/Y on an annual basis, as set out in the question.

Awesome, thanks for the explanation. I guess I’ll be doing this from now on as well, because, as stated in my original post; messing with P/Y and C/Y gave the wrong answers anyway.

[Pyng]

@breadmaker

@R44

So then what are the P/Y and C/Y functions useful for then?

Why is it that I can’t just input all the calculations like they are in the problem, and then simply tell the calculator that it is compounded twice a year? Should this not give the same outcome?

Kind regards

Some candidates like to leave P/Y=C/Y=1 for ALL TVM problems because they don’t want the hassle of changing these values. You can do it this way, but you have to be very careful how you set the interest rate I. This is particularly a problem where the payment frequency and the compounding frequency don’t match. That’s why I tend to go with setting P/Y and C/Y on an annual basis, as set out in the question.

What if the question is: Invest $1000 at the end of every quarter for 1 year at rate of 10% compounded semi annually. What is FV?

i = 10% (Compounded Semi annually)

PMT = 1000 (At the End of every quarter)

N = 1 year multiply by 4 = 4 payments

How do you approach this question without using C/Y and P/Y on calculator? Is FV on calculator the correct answer?

(The calculator gives FV as 4,150.6249 by inserting C/Y = 2 and P/Y = 4)

[Pyng]

@Pyng

@breadmaker

@R44

So then what are the P/Y and C/Y functions useful for then?

Why is it that I can’t just input all the calculations like they are in the problem, and then simply tell the calculator that it is compounded twice a year? Should this not give the same outcome?

Kind regards

Some candidates like to leave P/Y=C/Y=1 for ALL TVM problems because they don’t want the hassle of changing these values. You can do it this way, but you have to be very careful how you set the interest rate I. This is particularly a problem where the payment frequency and the compounding frequency don’t match. That’s why I tend to go with setting P/Y and C/Y on an annual basis, as set out in the question.

What if the question is: Invest $1000 at the end of every quarter for 1 year at rate of 10% compounded semi annually. What is FV?

i = 10% (Compounded Semi annually)

PMT = 1000 (At the End of every quarter)

N = 1 year multiply by 4 = 4 payments

How do you approach this question without using C/Y and P/Y on calculator? Is FV on calculator the correct answer?

(The calculator gives FV as 4,150.6249 by inserting C/Y = 2 and P/Y = 4)

Just found out how the calculator works:

A. 1000(1.05)^1.5 = 1075.9298

B. 1000(1.05)^1 = 1050

C. 1000(1.05)^0.5 = 1024.6951

D. 1000

Total = 1,075.9298 + 1,050 + 1,024.6951 + 1,000 = 4,150.6249

[breadmaker]

If I wanted to keep P/Y=C/Y=1, what values would I enter into the calculator?

The proof is left as an exercise to the interested reader.

[Pyng]

Let me grab some popcorn first! This’s gonna be good.