By A. H. Pollard (Auth.)

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**Extra resources for An Introduction to the Mathematics of Finance**

**Sample text**

T h a t is. at any point in time, at 6°/0 interest, the two payments ire of equal value. T h e same holds true for any two equivalent sets of payments. 43 due in eight years' time since . . V. V. 54 also. T h e values of the two sets of payments at any point of time, at 6 % interest, are equal. If we have two such sets of payments which, at some rate of interest, are of equal value, then any equation which expresses this equality of value at any time is called an equation of value. AMOUNT OF ONE PAYMENT UNKNOWN Problem 1: I n return for $700 at the end of 12 years, a m a n agrees to pay $200 at the end of two years, $300 at the end of eight years a n d a further sum at the end of 14 years.

W e assume the real rate of interest being charged, /, has been calculated (as in the previous section). As soon as the fourth instalment (say) has been made, the outstanding debt is the present value of the remaining instalments namely . . 20 obtained above u n d e r the rule of 78. I n practice the debtor is often (for good reason) asked to pay more than the figure calculated in this way to discharge his indebtedness. Problem: A loan of $300 for 5 years at 10% "flat" is repayable by monthly instalments.

60 + 59 + 58 + 57 + . . 80 1830 (48 + 47 + 46 + 45 + . . + 37) 1830 (36 + 35 + 34 + 33 + . . 00 1830 (24 + 23 + 22 + 21 + . . + 13) 1830 ( 1 2 + 11 + 10 + 9 + . . e. 50) and the o u t s t a n d i n g debt column by subtracting the principal repaid figures progressively from $300. C O N T R A C T S A T "FLAT" RATES OF INTEREST 53 I n practice, ta'bles are available from which the results u n d e r the "rule of 78" may be written down. It is useful, however, to realize the assumption on which it is based and the degree of inaccuracy involved.