INTEREST, the payment due by the borrowa a sum of money to the lender for i its use. The interest of £100 for one year is called the rate per cent; the money lent, the principal; and the sum of any principal and its interest, the amount. The current or market rate of interest fluctuates widely, by reason, not, as is often supposed, of the extent of•the supply of money, but of the variable rides of profit, as in Holland, where it has always been comparatively low, and in our own time in Australia and California, where mercantile profits being in excess, the into of interest is relatively high.
A strong prejudice against exacting interest existed in early times. arising from a mistaken view of some enactments of the Mosaic law;* and as late as the reign of Edward VI. there was a prohibitory act passed for the alleged reason that " the charg ing of interest was a vice most odious and detestable, and contrary to the word of God. ' Calvin, the famous reformer, was one of the first to expose the error and impoliey of this view, although a series of enactments, known as the usury laws, to sonic extent perpetuated it, by II 11 attempted restriction of the maximum rate to he paid, In Eng-, hunt this rate was fixed by act 21 James I. at 8 per cent. During the commonwealth it' was reduced to 0 per cent; and by the act 12 Anne, c. 19, to 5 per cent, at which rate it stood till 1839, when the law was repealed. In Scotland any charge for interest was prohibited before the reformation. In 1587 the rate was fixed by law at 10 per cent; in 1633 at 8 per cent; in 1661 at 6 per cent; and by the net of Anne, as above noted, at 5 per cent. It is now admitted that the operation of such laws tended only to raise the real rate of interest, by driving men in distress to adopt extravagant methods of raising money—the bonuses thus paid being really and in effect an addition' to the nominal interest.
Interest is computed on either of two principles: 1. Simple interest, where, should the interest not be paid as due, no interest is charged upon the arrears. Although this mode of reckoning has little to recommend it in reason, it is adopted in many transac tions, and receives the sanction of the law. The computation of simple interest is easy, it being only necessary to calculate the product of the principal, the rate per cent, and the period in years and fractions of a year, the result, divided by 100, giving the sum required. Thus, wanted the interest of £356 6s. 8d. for 31- years at 4 per cent.
356i X 31 X 4 100 = £49 17s. 9d.
2. Compound interest is the charge made where—the interest not being paid when due— it is added to the principal, forming the amount upon which the subsequent year's interest is computed. The rules for most readily making computations by compound
interest can only be effectively expressed algebraically, and, using the symbols in article DISCOUNT, we annex a few of the elementary formulae.
1. Since £1, increased by its interest r, at the end of one year becomes 1 -f-r, this amount at the end of the second year becomes (1 and generally at the end of the nol year (1 + r)°. Example: To find the amount of £1, improved at 3 per cent for six years. r, the interest for £1, is .05, and n = G; therefore 1.34, or £1 6s. 94d. 2. Since £1 becomes in one year 1 -I-r, it is found by ordinary proportion that the frac tion of £1 which will amount to £1. in a year is (1 +r) ' (i.e., + = a; and masoning as above, the sum which will amount to £1 n years hence is (1 -1-r) ° = r. 3. The amount of £1 in n years being (1 + r)", it will be seen that the excess of this sum over the original £1 invested, or (1 + r)' — 1, is the amount of an annual increment or "annuity" of for the period, and from this, by proportion, is deduced the formula for the amount of an annuity of £1 for the same time, being + r)° — 1.
4. Reasoning, as in (3), the present value of an annuity certain of £1 for n years, or the sum which, improved at interest, will meet the annuity is 11 1 — [1 r • Tables for the four classes of values above described, based on various rtes of interest, are given in most works on annuities.. Those by ,Mr. Rance are computed for each quarter per cent from to 10 per cent. It may be useful to note two results that can be easily deduced from a table of the present values of annuities (4). 1. The annuity which £1 will purchase for any number of years is the reciprocal of the corresponding value in such a table. Example: A person borrows £100, to be repaid by annuity in 15 years, with interest at 5 per cent; required the annuity? The present value of au annuityof £1 per annum for that period, at the rate stated, is £10.3S, and 100 X 10.38 ' = 9.6342 = 12s. 81d. 2. To find the annuity which in a given period will amount to Li—subtract from the annuity that £1 will purchase, ascertained as above, r, the interest of £1 for a year. Example: The annuity which, paid for 15 years, will amount to £1, taking interest at 5 per cent, is— Value of annuity which £1 will purchase as last found.. £.096242 Subtract r, at 5 per cent .030000 Annuity required £. 0i-6' 342 Or £4 12s. 8id. will amount iu 15 years to £100.