
When an investor purchases a bond in the secondary market at a discount, the discount must be accreted over the remaining life of the bond. The accretion of the discount will result in a higher yield to maturity. When an investor purchases a bond in the secondary market at a premium, the premium must be amortized over the remaining life of the bond. The amortization of the premium will result in a lower yield to maturity.
In order to calculate the bonds approximate yield to maturity, use the following formulas:
For a bond purchased at a discount use:
(Annual Interest + Annualized Discount) / (Price Paid + PAR) / 2
The Annualized discount is found by taking the total discount and dividing it by the number of years remaining until maturity. For example, let’s assume an investor purchased a 10% bond at $900 with 10 years until maturity. The bonds approximate yield to maturity would be found as follows:
$100 + $10 / $900 + $1,000 / 2
In this case the bond’s approximate yield to maturity is 11.57%.
For a bond purchased at a premium use:
(Annual Interest  Annualized Premium) / (Price Paid + PAR) / 2
The Annualized premium is found by taking the total premium and dividing it by the number of years remaining until maturity. For example lets assume an investor purchased a 10% bond at $1,100 with 10 years until maturity.
The bonds approximate yield to maturity would be found as follows:
$100  $10 / $1,100 + $1,000 / 2
In this case the bond’s approximate yield to maturity is 8.57%
Calculating the Yield to Call
In the event that the bond may be called in or redeemed by the issuer under a call feature an investor may calculate the approximate yield to call by using the approximate number of years left until the bond may be called.
Take note: The yield to call will always extend past the yield to maturity. The yield to call will always be the highest yield on a bond purchased at a discount and it will always be the lowest yield for a bond purchased at a premium.
Maturities

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