bought at a discount are treated exactly the same way, except that the
book value of the investment is constantly being added to instead of being
reduced. The amount added to the book value at each interest period
is called ACCUMULATION or ACCREDITION of the bond discount.
The appended table (Mathematics of Accumulation) illustrates the
mathematical history of a bond bought at a discount and carried currently
on an investment basis, e.g., a 3.0% bond, paying interest semi-annually
March 1 and September 1, with four-year maturity, bought March 1, 1978
to yield 4.5%, or a cost of $945.60.
yield is determined by multiplying the book value, which in the first
instance is the purchase price, by the predetermined yield, or basis rate,
4.5%. The net income for
September 1, 1978, therefore, is determined by multiplying $945.60 by
2.25%. This is $21.30. The difference between $21.30 (yield or net income) and $15.00
(cash interest) is $6.30, which is the first accumulation increment to
be applied in accretion of the book value of the investment.
The new book value for September 1, 1978, is the summation of $945.60
and $6.30, or $951.90. Since the book value is constantly being increased, the net
income for each subsequent interest period rises. It will be noted that the total of the accumulation is equal
to the total of the original discount in price of the bond and that provision
has been made to accumulate it completely.
entry on the books for the first interest period should be as follows: