## Coupon rate calculation

Item Quantity Price Action
\$
\$
\$
\$
\$

You can find coupon rate of a bond by using this calculation tool when you provide maturity value, bond price, market rate of return also known as YTM, years to maturity, and number of interest payments paid by the bond issuer. The compounding of interest may be either periodic or it may be continuous.

### Coupon rate formula

CR = n[ (P - M (1+r)^-N ) / ( M { 1 - (1+r)^-N } / r ) ]
where CR is the coupon rate
n is the number of interest payments per year
P is the market price of the bond
M is the par value or maturity value of the bond
r is the periodic rate of return
N is the total number of interest payments

### Coupon rate calculation

Here is an coupon rate example calculation for \$1000 par value with 4 years to maturity left. The current market price of this bond is \$1036.30 and similar bonds on the market have a rate of return (YTM) of 4%. Using the formula listed in earlier section we will find the coupon rate of this bond that makes annual coupon payments.

n = 1
i = 4% / 1
P = 1036.3
M = 1000
N = 4 * 1

n [ P - M * pvif(i, N) ] / [ M * pvifa(i, N) ]
1 [ 1036.3 - 1000 * pvif(0.04, 4) ] / [ 1000 * pvifa(0.04, 4) ]
1 [ 1036.3 - 1000 * 0.85480419103 ] / [ 1000 * 3.62989522426 ]
1 [ 1036.3 - 854.80419103 ] / 3629.89522426
1 [ 181.49580897 ] / 3629.89522426
181.49580897 / 3629.89522426
0.0500002886467
Coupon rate = 5.000%

As the results show, this particular bond makes an annual coupon payment at a rate of 5%.

### Semi-annual compounding

In the previous example, the bond made annual coupon payments which is quite common with bonds that are issued in Europe. Whereas most or all bonds that are issued in the U.S. make interest payments twice a year, this leads to semi-annual compounding of interest. Obviously price of a semi-annual bond differs from that of the bond that makes annual interest payments. Now I will move forward with showing you finding coupon rate when interest payments are made twice a year. This bond has a market price of \$956.24 with 5 years remaining to maturity. Similar bonds in the market have a yield of maturity of 5%.

n = 2
i = 5% / 2
P = 956.24
M = 1000
N = 5 * 2

n [ P - M * pvif(i, N) ] / [ M * pvifa(i, N) ]
2 [ 956.240 - 1000 * pvif(0.025, 10) ] / [ 1000 * pvifa(0.025, 10) ]
2 [ 956.240 - 1000 * 0.781198401726 ] / [ 1000 * 8.75206393097 ]
2 [ 956.240 - 781.198401726 ] / 8752.06393097
2 [ 175.041598274 ] / 8752.06393097
350.083196549 / 8752.06393097
0.0400000730467
Coupon rate = 4.000%

Coupon rate calculation
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## Related Content

• You were presented with a detailed illustration of coupon rate calculation and now you can press ahead to view another detailed demonstration for bond YTM calculation. It will be required of you to enter the market price of bond and an annual coupon rate along with remaining years to maturity and the par value. But then if you are seeking just the YTM without any regards for how it is calculated then this YTM calculator will do it for you.

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