# Zero-Coupon Bond Yield To Maturity (YTM)

Updated: Mar 7, 2021

How do I find the YTM of a zero-coupon bond? A zero-coupon bond pays no coupons and instead, the profit made from investing in a zero-coupon bond is a result of the difference between the purchase price and par value. In other words, a zero-coupon bond does not many regular payments, it essentially only makes one and it is the par value of the bond.

There are two ways:

1) Use a financial calculator

2) Use a formula for zero-coupon bond yield

**1) Find the YTM of a zero-coupon bond using a financial calculator**

Example:

You buy a zero-coupon bond with a par value of $100 for $97. The bond matures in 2 years and 6 months.

How to Solve YTM

Enter the Following into your financial calculator

Enter 2.5 then push N

Enter -97 then push PV

Enter 0 then push PMT

Enter 100 then push FV

push CPT (top left of BAII PLUS)

push I/Y

**The Answer = 1.22582%**

**The YTM of the zero-coupon bond is 1.22582%**

*Check:*

*$100/(1.0122582^2.5)=$97*

**2) Find the YTM of a ****zero-coupon**** bond using a formula**

Formula:

YTM +1 = (par value / purchase price) ^ (1/n)

*Test *

*(100/97)^(1/2.5) = YTM+1*

*1.0122582 = YTM+1*

*1.22582% = YTM*

**The Answer = 1.22582%**

**The YTM of the zero-coupon bond is 1.22582%**

**Dealing with periods of less than a year?**

In order to calculate the YTM of a bond maturing at a period other than a round year or half-year simply add the fraction of a year to n.

For example, if a bond matures in 725 days we could simply divide 725/365 to find our n value. In this case, it would be 1.98630