14th  Top actuarial topics 
The Yield to maturity (YTM) or redemption yield of a bond or other fixedinterest security, such as gilts, is the internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule. Yield to maturity is actually an estimation of future return, as the rate at which coupon payments can be reinvested when received is unknown.^{[1]} It enables investors to compare the merits of different financial instruments. The YTM is often given in terms of Annual Percentage Rate (A.P.R.), but more usually market convention is followed: in a number of major markets the convention is to quote yields semiannually (see compound interest: thus, for example, an annual effective yield of 10.25% would be quoted as 5.00%, because 1.05 x 1.05 = 1.1025).
The yield is usually quoted without making any allowance for tax paid by the investor on the return, and is then known as "gross redemption yield". It also does not make any allowance for the dealing costs incurred by the purchaser (or seller).
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As some bonds have different characteristics, there are some variants of YTM:
Consider a 30year zerocoupon bond with a face value of $100. If the bond is priced at an (annual) yieldtomaturity of 10%, it will cost $5.73 today (the present value of this cash flow, 100/(1.1)^{30} = 5.73). Over the coming 30 years, the price will advance to $100, and the annualized return will be 10%.
What happens in the meantime? Suppose that over the first 10 years of the holding period, interest rates decline, and the yieldtomaturity on the bond falls to 7%. With 20 years remaining to maturity, the price of the bond will be $25.84 (100/(1.07^20). Even though the yieldtomaturity for the remaining life of the bond is just 7%, and the yieldtomaturity bargained for when the bond was purchased was only 10%, the return earned over the first 10 years is 16.25%. This can be found by evaluating (1+i) = (25.842/5.731)^{0.1} = 1.1625.
Over the remaining 20 years of the bond, the annual rate earned is not 16.25%, but rather 7%. This can be found by evaluating (1+i) = (100/25.84)^{0.05} = 1.07. Over the entire 30 year holding period, the original $5.73 invested increased to $100, so 10% per annum was earned, irrespective of any interest rate changes in between.
Here is another example:
You buy ABC Company bond which matures in 1 year and has a 5% interest rate (coupon) and has a par value of $100. You pay $90 for the bond.
The running yield is 5.56% (5/90*100).
If you hold the bond until maturity, ABC Company will give you $5 as interest and $100 for the matured bond.
Now for your $90 investment you made $105 and your yield to maturity is 16.67% (= 105/901)

