Question

how to convert fraction into years
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Answer 1

Year fractions are frequently used in interest calculations, like for example the calculation of the price of a bond. When calculating the price of a bond, all of the security's future cash flows are discounted at the bond's yield using the time span between the value date for the bond price calculation and each of the cashflows' payment date. Whenever the value date is not an anniversary date of the bond's maturity date, the discounting period will comprise a year fraction.

Example:

Let's consider a bond which matures on Dec 15th, 2016 and bears a 3% coupon. The bond redeems at par, has an actual/actual daycount convention and the value date used for calculating the price shall be July 15th, 2015.

The bond will pay three cashflows until maturity, one coupon on Dec 15th 2015 and the final coupon and the principal both on Dec 15th, 2016.

The discount period for the first coupon is calculated by dividing the number of remaining days between the value date (July 15th) and the coupon date (Dec 15th) by the number of days for the interest period: 153 / 365 = 0.419178082. The result is the year fraction which we will also use for determining the discount period of the two cashflows on Dec 15th, 2016.

As these cashflows are a full year later, we simply add 1, which gives us a discount period of 1.419178082 for the last coupon and the bond's principal.

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