INTEREST. 271. The payment made for the use of money lent for any length of time is called Interest, and is usually reckoned at so much for £100 during a year; if the interest of £100 for a year be £5, the money is said to be lent at 5 per cent. per annum, and 5 is called the rate of interest. The money lent is termed the principal, and the sum of the interest and principal is called the amount. 272. The rate is a conventional agreement between the lender and the borrower of the principal. There is, however, a limit, beyond which the rate is illegal. Usurers are those who lend money at a higher rate than the law permits. 273. The learner must remember that 4 per cent. does not signify only that the interest of £100 is £4, but it means as well that the interest of 100s. is 4s., or that the interest of 100 farthings, is 4 farthings; in fact, it implies that the interest of 100 units is 4 units of the same kind. 274. The interest depends, then, on the principal, the time that the principal is lent, and the rate. 275. Interest is of two kinds; if the borrower pays the interest at a specified period, either yearly, half-yearly, or quarterly, according to agreement, it is called Simple Interest; but when at the end of any stated time, as a year, &c., the interest is added to the principal for the second year; and again, the interest accruing being added to the last principal, &c., it is called Compound Interest. 276. There are five quantities concerned in interest, the principal, the rate, the time, the interest, and the amount, any three of these, (except the principal, the interest, and the amount) being given, the others can be found. 277. Therefore, we have to consider the four following cases: 1st, to find the interest of a given principal, for a given time, at a given rate. 2nd, to find the rate, when the principal, the interest, and the time are given. 3rd, to find the time when the rate, the principal, and the interest are given. 4th, to find the principal, when the time, the interest, and the rate are known. 278. 1st case: Find the simple interest of £240. 10s. for 1 year, and also for 6 years, at 4 per cent. 100 in 1 year gains 4. To or .04. 240.5 × £.04, or £9. 12s. 43d. £240.5 6 years gains 240.5 × £.04 × 6 or £57. 14s. 4 Ex. 2. What is the interest of £500. 13s. 4d. for 24 years, at 23 per cent? Here 100 in 1 year gains 2.75. .. 1 in 1 year gains .0275. ..£500 in 2 yrs. gains 500 x 2.75 x £.0275= £37.17s. 3 d. Operation: .0275 2.75 1375 1925 550 .075625 500 37812500 25208 37.862916 13 4 20 17.258333 12 3.100000 Answer, £37. 17s. 3d, Ex. 3. Required, the interest of £365. 4s. 10d. for 2 years Ex. 4. Find the interest of £140. 10s. for 76 days, at 5 per These questions will afford many opportunities of abbreviating the work, but for that the pupil must be well grounded in fractions; he must be able to detect at a glance that by transforming an expression he may often obtain another more convenient to use. In the first and second examples we have introduced some decimals, which make the process very simple. The third example has been worked by practice; and in the second line of the solution of the last example, we have adopted a transformation, in order to facilitate the division. 279. 2nd case. Ex. 1. At what rate per cent. must £102. 10s. be lent, so that the interest may be £12. 13s. 84d. in 2 years? £102. 10s. in 2.25 years gains £12. 13s. 84d., ..£100 in 1 year gains 10×£12. 13s. 8‡d. 102.5 x 2.25 4.1 5 Ex. 2. If £1 amounts to £1. 2s. 9d. in 34 years, at what rate per cent. must it have been lent? Here interest = £1. 2s. 9d.-£1=2s. 9d. £1 in 34 years gains 2s. 9d., or 33d., 280. 3rd case. Ex. 1. In what time will £300 amount to £350. 12s. 6d., at 33 per cent. per annum? Here interest = £350. 12s. 6d-£300 £50. 12s. 6d. 33 is gained by 100 in 1 year, ..1 is gained by 1 in 100 x 1 ..£50. 12s. 6d. is gained by 300 in Ex. 2. In what time will £818. 18s. 4d. amount to £1245. 5s., at 33 per cent. ? Here interest = £1245. 5s.-£818. 18s. 4d. = £426. 6s. 8d. .33 is gained by 100 in 1 year, 4 yr. £426. 6s. 8d. is gained by 818. 18s. 4d. in 1×100×426} =138 yrs. nearly. 33 × 8181 |