## Coupon Rate and Current Yield?

### Coupon Rate and Current Yield?

Coupon Rate and Current Yield?

**slkusractJohn**

The coupon rate is just $80/$1,000 = 0.08 or 8% of the face value. The yield is the IRR of the cash flow. Given that the coupons are fixed amounts at a regular interval you can simplify the IRR with the summation of a geometric sequence equation such that the rate R satisfied the following equation: $900 = $80 * { summation of the term (1/R)^k for k = 1 to 20 } + $1,000 / R^20 .: $900 = $80 * ( ( 1 - 1/R^21 ) / ( 1 - 1/R ) - 1 ) + $1,000 / R^20 This is a 21st order roots of a polynomial problem so it has be solved iteratively, perhaps by Newton Raphson, Secant method or just by a binary tree. Excel also has an =IRR() function if you don't mind typing in -900, followed by 19 cells of the value 80 and one cell with the value of 1080. For this case it's R = 1.0910356 therefore the yield to two decimal points in percentage is 9.10% per annum.

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