what is the formula for YTM for semiannual payments using handheld calculator ?? how can i able to calculate yield to maturity for semiannual bond payments with handheld calculator
From InvestingAnswers, the price of a bond is equal to the present value of its future cash flows, as shown in the following formula:
P = price of the bond n = number of periods C = coupon payment r = required rate of return on this investment F = maturity value t = time period when payment is to be received
By induction, this is equivalent to:
p = ((1 + r)^-n * (f * r + c * ((1 + r)^n - 1))) / r
or, using more familiar formulae, it is equivalent to the formula for the present value of an ordinary annuity to represent the coupon payments, plus a term for the discounted value at maturity:
p = ((c - c * (1 + r)^-n) / r) + f * (1 + r)^-n
For example, a 10 year semiannual bond with coupon payment 10%, priced at 1095 with maturity value 1000.
p = 1095 n = 10 * 2 = 20 f = 1000 c = f * 0.10 / 2 = 50 1095 = ((1 + r)^-20 * (1000 * r + 50 * ((1 + r)^20 - 1))) / r
r yields 0.0428332 or 4.28% semi-annually. (8.75% per annum)
The solution can be found by plotting or using a solver, which many pocket calculators have.
p as a function of
r, intersecting with
p = 1095 when
r = 0.0428
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