YTM - yield to maturity

f(i) = 1000 + -1100 * (1+i)^20 + 20 [(1+i)^20 - 1]/i f'(i) = 20 * -1100 * (1+i)^19 + 20 * (20 i (1 + i)^19 - (1 + i)^20 + 1) / (i^2)

i = 0.1
f(i) = -5254.75
f'(i) = -121541.3627
i1 = 0.1 - -5254.75/-121541.3627 = 0.05676574758247
Error Bound = 0.05676574758247 - 0.1 = 0.043234 > 0.000001

i1 = 0.05676574758247
f(i1) = -1608.0563
f'(i1) = -55210.0058
i2 = 0.05676574758247 - -1608.0563/-55210.0058 = 0.027639571995785
Error Bound = 0.027639571995785 - 0.05676574758247 = 0.029126 > 0.000001

i2 = 0.027639571995785
f(i2) = -372.9307
f'(i2) = -31620.5576
i3 = 0.027639571995785 - -372.9307/-31620.5576 = 0.015845641616611
Error Bound = 0.015845641616611 - 0.027639571995785 = 0.011794 > 0.000001

i3 = 0.015845641616611
f(i3) = -40.0796
f'(i3) = -25057.7742
i4 = 0.015845641616611 - -40.0796/-25057.7742 = 0.014246154392232
Error Bound = 0.014246154392232 - 0.015845641616611 = 0.001599 > 0.000001

i4 = 0.014246154392232
f(i4) = -0.632
f'(i4) = -24271.3312
i5 = 0.014246154392232 - -0.632/-24271.3312 = 0.014220114627777
Error Bound = 0.014220114627777 - 0.014246154392232 = 2.6E-5 > 0.000001

i5 = 0.014220114627777
f(i5) = -0.0002
f'(i5) = -24258.7174
i6 = 0.014220114627777 - -0.0002/-24258.7174 = 0.014220107857248
Error Bound = 0.014220107857248 - 0.014220114627777 = 0 < 0.000001

Periodic YTM = 1.42% Nominal YTM = 2.84% Annual effective yield = 2.86%

Using tadXL function such as tadBYTM finding yield to maturity in Excel 2007, 2010 and 2013 becomes really easy. Let us now briefly look at the financial functions in tadXL to find YTM using Excel:

=tadBYTM( years_to_maturity, coupon_rate, bond_price, par_value, compounding )