# How do I calculate yield-to-maturity (YTM) with a simple handheld calculator for semiannual payments?

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

• Why do you believe that such a formula exists? – DJohnM Aug 3 '15 at 20:54

From InvestingAnswers, the price of a bond is equal to the present value of its future cash flows, as shown in the following formula: Where:

``````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
``````

Solving for `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. Plot of `p` as a function of `r`, intersecting with `p = 1095` when `r = 0.0428`  Checking on Investopedia If it's number of years and the interest is per-annum the formula is the same as the normal one.

this should work on most hand-held calculators.

``````rate ÷ 100 + 1 = x
{now press = once for each year past the first}
x principle =
``````

R = I ^ P

R = return (2 means double)

I = (Intrest rate / 100) + 1 [1.104 = 10.4%]

P = number of periods (7 years)

2 = 1.104 ^ 7 (you double your money in seven years with a yearly Intrest rate of 10.4%)

I = R^(1/P)

1.104 = 2^(1/7)

P = log(R) / log(I)

7 = log(2) / log(1.104)