# Bond's yield to maturity

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Consider a five-year, 1000 dollars bond with a 5% coupon rate and annual coupons. If this bond is currently trading for a price of 957.35 dollars, what is the bond's yield to maturity?

F = 1000 dollars
c = 0.05
P = 957.35 dollars
N = 5 years
y = ?

I used the formula presented here for the yield-to-maturity calculation. The equation looks like this:

$$957.35 = \frac{1050}{(1+y)^5} + \frac{50}{(1+y)^4} + \frac{50}{(1+y)^3} + \frac{50}{(1+y)^2} + \frac{50}{(1+y)}$$

From that y = 6%.

What is the meaning of that number (6%)? The cash-flow is:

Receive first coupon after 1 year: 50 dollars
Receive second coupon after 2 years: 50 dollars
Receive third coupon after 3 years: 50 dollars
Receive fourth coupon after 4 years: 50 dollars
Receive fifth coupon and nominal value after 5 years: 1050 dollars

I cannot obtain 6% when dividing any combination of these numbers. So what is the meaning of that 6%?

tnich
Homework Helper
Consider a five-year, 1000 dollars bond with a 5% coupon rate and annual coupons. If this bond is currently trading for a price of 957.35 dollars, what is the bond's yield to maturity?

F = 1000 dollars
c = 0.05
P = 957.35 dollars
N = 5 years
y = ?

I used the formula presented here for the yield-to-maturity calculation. The equation looks like this:

$$957.35 = \frac{1050}{(1+y)^5} + \frac{50}{(1+y)^4} + \frac{50}{(1+y)^3} + \frac{50}{(1+y)^2} + \frac{50}{(1+y)}$$

From that y = 6%.

What is the meaning of that number (6%)? The cash-flow is:

Receive first coupon after 1 year: 50 dollars
Receive second coupon after 2 years: 50 dollars
Receive third coupon after 3 years: 50 dollars
Receive fourth coupon after 4 years: 50 dollars
Receive fifth coupon and nominal value after 5 years: 1050 dollars

I cannot obtain 6% when dividing any combination of these numbers. So what is the meaning of that 6%?
This is called a Present Value calculation. It is used in investing and economics to find the present value of an investment, assuming a discount rate ##y##. This discount rate represents (in the case of investments) the going rate for interest on similar investments. If you buy a $1000 bond with a 5% face interest rate (i.e., it pays$50 per year), but the going rate is 6%, then the purchase price of the bond is discounted to compensate for the difference in the interest rate. The present value tells you how much you would need to invest at a 6% rate to generate the same returns at the same time intervals.

The present value tells you how much you would need to invest at a 6% rate to generate the same returns at the same time intervals.

And the 6% can be approximately obtained from this expression:
$$\cfrac{\cfrac{50+50+50+50+1050-957.35}{5}}{957.35}$$