# How to Amortize a Discount/Premium Bond

Updated: Aug 5, 2021

When a bond is purchased at a discount or premium the discount or premium is amortized for accounting purposes. In order to explain the process, we'll work through an example.

### Amortizing a Bond Purchased at a Discount

A bond has the following characteristics:

N = 5

IY= 9%

PV= -922.21

PMT= 70

FV = 1000

The bond is purchased for \$922.21. The interest we must earn on this investment is 9%. Therefore, the total interest income in each period must be the carrying value of the bond *.09, and for the first period, this is \$922.21 *.09 = \$83. In the first period, the interest income is \$83. The issue is that the actual payment in that period was only \$70. Where does the extra income come from? The amortization of the discount.

In order to determine the appropriate discount amortization in the period find the difference between interest income and coupon received. In the first year \$83-\$70 = \$13. This means that in the next period our carrying value will be \$922.21+\$13 = \$935.21. By repeating the process each year for 5 years we can observe the carrying value of the bond reaches \$1000.

### Amortizing a Bond Purchased at a Premium

A bond has the following characteristics:

N = 5

IY= 6%

PV= -1042.12

PMT= 70

FV = 1000

repeat the same process as before, this time interest - PMT will be a negative number which will reduce the carrying value of the bond. In this case the payment is greater than the interest income, the amortization of the premium makes this possible.