A Further Illustration Of Accrued Interest

Suppose, then, that a bond of £100 bearing interest at 3 per cent per annum, which is payable in half-yearly instalments on the 1st of January and July, is purchased on the 1st of April at the price of 90¾. This price, however, does not represent the value of the capital amount itself. For - omitting the consideration of extraneous circumstances which may affect the value of the bond, such as war, the extent of speculation, and many other circumstances - the value continuously increases after each payment of interest is made by the addition of the interest accruing. The interest for the half-year is £1 10s.; the proportion of this current interest from the date of the preceding payment to the time of purchase is one-half of £1 10s., or 15s. (since three months have expired); hence the capital value alone of the bond is 90, or the actual cost of 90¾, diminished by the accrued interest. This accrued amount is paid by the buyer to the seller, but the former recovers it when he himself receives the ensuing periodical payment of interest. The price accordingly given in this case by the investor consists partly of the value of the capital amount, and partly of interest which has grown. In other words, 90 should be entered in his capital account as the value of the investment, and 15s. in his interest account as a liability to be redeemed when the stated interest is next received.

A Practical Caution

This suggests a practical caution. When we compare, for purposes of buying and selling stocks, the return obtained from different classes of securities, in order to ascertain their relative dearness or cheapness - we must notice when the interest on each becomes periodically due (as some prices will include more accrued interest than others), and our decision of choice (so far as this point is concerned) will then proceed on a uniform basis of estimate.

II. The Return Derived From An Investment

The clearest and most conclusive exposition is frequently that which is not verbal (or what was termed by older writers, the rhetorical mode), but is presented in the form of concrete examples of actual instances.

One Method Of Computation When A Security Has Been Bought At A Discount

A bond for £100, bearing interest at the rate of 3 per cent per annum and redeemable at par (that is, at the amount expressed in the bond as the debt) at the end of thirty years from its issue, is purchased for £95 - the security thus, for various reasons adversely affecting its appreciation in the market, standing at a discount of 5 per cent. The return per cent which the buyer secures for each £95 so invested is obtained from the proportion: as £95 is to the £3 annually received, so is £100 to the actual return on the purchase money, which works out at about £3 3s. 2d. per cent. But at the end of the term of the currency of the bond the holder receives £100 for his £95, or a bonus of £5 in respect of each £100 of the bond. Assume that he bought it five years after its issue, so that the unexpired period is twenty-five years. Now £1 a year will (at, let us suppose, 3 per cent as a safe rate) accumulate to £36 9s. 2d. by the end of twenty-five years; hence by proportion 2s. 9d. per annum will accumulate to the £5 in question. In this aspect of the case the purchaser may be regarded as receiving, (1) the £3 a year of interest, and (2) this additional annual sum of 2s. 9d., for this sum, as has been shown, is the yearly equivalent during the term of the extra amount to be actually received at the end. These two together amount to £3 2s. 9d. for the purchase price of £95, and reduced to a return per cent (as £100 is to the actual rate yielded, so is £95 to £3 2s. 9d.) the total return is ascertained to be £3 6s. per cent upon the money he has invested, instead of £3 3s. 2d. In this mode of considering the result of the investment it will be observed that the holder has taken into actual account the annual equivalent of his ultimate bonus, and must accordingly in this manner of survey remember that for the £95 expended (yielding him £3 6s.) he is only to regard the receipt of £95 upon redemption. He will as a fact obtain £100, but £5 of it has been used up in this mode of reckoning; in other words, this method of consideration gives him a final refund of the £95 he has actually invested, and an income meantime at the rate of £3 6s. per cent per annum.