What is the price of perpetuity for a bond that pays $20 each six months with a semi-annual interest rate of 10%?

Price = PMT/k

You can think about price in this equation the same way we valued perpetuity in quantitive methods. We divided the payment by the correct periodic rate, so:

Price = 20/(.1/2). (As you get payments semiannually, so the correct rate is the annual rate divided by 2)

So the price is 400

Thank you for reply, I still don’t understand that why don’t we divide by semi-annual interest rate?

20/0.1 = 200

Yeah you have to be careful with these types of problems. What it looks like they gave you in this problem is a stated annual rate, which is how much interest you earn in a year without the effects of compounding. The issue is that your bond pays every 1/2 year, so we need the rate of interest earned every 1/2 year. So to get that we divide the stated annual rate by two.

In almost all of the questions I’ve seen, you are given the stated annual rate, and if not it is indicated somewhere in the question (so you will know, or should know, it’s something different).

Did that help?

If I understood you correctly, you are saying that the semi-annual interest rate as the problem states should be divided by two as its apparently stated annual rate. This is the part I don’t get. Would the problem be the same if we replaced semi-annual interest rate with annual rate of 10%?

It’s a stated annual rate that compounds semi annually.

So the discount rate you use per compounding period would be 10%/2 = 5%

If your perpetuity made payments quarterly, then the discount rate you would use would be 10%/4 = 2.5%

You have to make the periodicity of the discount rate you are using and how often you receive payments yearly match. You were given a discount rate with a periodicity of 1 (annual discount rate). Your perpetuity had a periodicity of 2 (semiannual payments). Dividing the annual rate by two makes these match.

Rates are always stated annualised

On the BAII

P/Y=C/Y=2

9,999 N (not infinity, but close enough), 10 I 20 PMT CPT PV -400

Hello,

But in this question, it is mentioned rate is semiannual.

“With a semi-annual interest rate of 10%”

Can u elaborate?