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In considering Indian Railway Securities as investments it is advisable to have a knowledge of the history of the railways. The first lines to be built in India were constructed by Companies on land supplied free by the East India Company, who also guaranteed that a certain rate of interest should be paid each year on the capital expended with their approval. This arrangement was made with the idea of attracting Companies to build lines, and in return the East India Company had the right to exercise a certain amount of supervision and control and also had certain options of purchase. When in a position to do so, the Companies repaid each year, to the extent of one half the excess net earnings in that year, any amounts paid by the East India Company under the guarantee arrangements.
page 29 note * Another, and from the Student's point of view, probably simpler way of finding the amount of accrued interest included in the purchase price is to ascertain the interest yielded by the Investment to the purchaser; and then to value the Security at the same rate of interest, immediately after the last payment of the Annuity. The difference between this value and the purchase price is the accrued interest.
If i = nominal rate of interest per annum convertible half-yearly.
t = fraction of the half-year from the date of last Annuity payment to the date of purchase.
n = number of half-years (unexpired term) from the date of the last Annuity payment.
Purchase price . . = 
.
Value at date of last Annuity payment = 
.
Accrued interest = 
where the annuity value in each case is calculated at the effective rate of interest 
.
The Book Value after writing off the accrued interest from the purchase price is thus and the amounts by which this is to be written down as each payment of annuity is received are vn
, vn−1
, … respectively. [Editor.]
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