tion; or, since the rate per cent. is generally a small number, it may be simpler, in finding the payment to be made, to multiply by the rate per cent. and divide by 100. Ex (1) Find the commission on buying goods to the amount of £5235, at 1 per cent. £5235 5235 2617 10 78.52 10 20 10'50 I 2 6'00 Ans. £78 10s. 6d. Ex. (2) Find the premium for insuring a cargo worth £8365 at 64 per cent. £8364 50190 2091 5 522.81 5 20 16°25 I 2 3:00 Ans. 522 16s. 3d. Ex. (3) For what sum, in the above case, should the cargo be insured, so that in the event of loss, the owner may receive back both the value of the cargo and the premium? Here, 100 representing the sum insured, we shall have, in the event of loss, 100 as the representative of the sum paid as indemnity to the owner. Of this, 6 represents the premium he had paid; therefore 100-61, i. e. 93, is the representative of the value of the cargo. Hence, in order to find the amount to be insured, we shall have the proportion The premium to be paid must therefore be 6 per cent. on this amount, and may be found to be £557 138. 4d. Exercise 64. (1) What commission, at 2 per cent., would be charged on £3272 IOS.? (2) At 2 per cent., what premium of insurance would be paid on a vessel worth £7280? (3) Find the premium to be paid for insuring a person's life for £2500 at an age for which the rate is £2 18. 3d. per cent. (4) What premium must be paid for fire insurance at 35. per cent. on property valued at £2731 58.? (5) Find the profits which must be realised in order that on a capital of £15275 the return may be 11 per cent. (6) What premium must a person at the age of 24 pay for insuring his life for £1500, the rate at that age being £1 16s. 3d. per cent.? (7) What sum will be deducted for cash payment of a bill of £18 2s. 6d., if discount is allowed at 4 per cent.? I (8) Find the brokerage at per cent. to be paid on £10450. (9) A dividend of 4 per cent. is paid by a railway; how much will a person receive who has £960 invested in it? (10) A vessel with its cargo is worth £12052; determine the sum to be insured, and the premium to be paid at 1 per cent., so that in the event of loss the owner may receive back both the value of the vessel and the premium. (11) Find the ready money payment for a bill of £52 7s. 6d. when discount of 6 per cent. is allowed for cash. (12) A vessel is lost worth £19266 10s., the owners having insured it so as to recover both the value and the premium at 3 per cent.; what premium did they pay and what sum will they receive? (13) Find the commission on £4324 16s. at 64 per cent. (14) If the rent paid for a house is to be 6 per cent. on the cost, what will it amount to when the cost has been £1720? (15) A railway company pays a dividend of 3 per cent. for the first half of a year, and 44 for the second half : what income will a person receive for the year who has £825 invested? (16) A person pays a premium of £144 18. 10 for insuring £3842 108., at what rate per cent. is he charged? (17) If a premium of insurance at 23 per cent. amount to £28 128. find the sum insured. (18) Find the premium of insurance for £2650, for a person 50 years of age, the rate for that age being £4 10s. 6d. per cent. (19) A person has £19280 invested in a business; what is the difference in his income for two years for which the returns are 9 per cent. and 72 per cent.? (20) A vessel is so insured that if lost the owner may receive both the value of the vessel and the premium. The value of the vessel being £96084, and the rate of insurance 1 per cent., find the premium. CHAPTER XI. INTEREST AND DISCOUNT. 80.-INTEREST is the payment made for the use of money. The interest to be paid for the use of a given sum differs from the payments considered in the last chapter, inasmuch as it depends on the time for which the sum is lent as well as on the rate per cent. charged. The sum lent is called the Principal. The rate per cent. is the per centage paid on the principal for one year. In the same manner as was explained in the last chapter, the rate per cent. may be considered as the number of pounds payable for the use of £100 for a year. The principal and interest added together are called the Amount. SIMPLE INTEREST. 81.-When the interest is paid each year only on the given principal, it is called Simple Interest. To find the simple interest on a given principal for a year. RULE.-Multiply the principal by the rate per cent., and divide by 100. To find the simple interest on a given principal for any given time. RULE.-Express the time in years or as the fraction of a year, and multiply the interest for one year by this. N.B.-The two rules may often for shortness be applied together as in Ex. (2). It will be seen that 100 being the representative of the principal, the rate per cent. will represent the interest for a year, the product of the rate per cent. and the number of years will represent the whole interest, and this added to 100 will represent the amount. Thus if the time be 5 years, and the rate per cent 4, the interest will be represented by 20, and the amount by 120. Ex. (1) Find the interest on £924 12s. 6d. for 5 years at 3 per cent. £924 12s. 6d. Ex. (2) Find the amount of £750 lent on March 29th and repaid Aug. 28th at 5 per cent. Here the time=2+30+31+30+31+28 days. =152 days. (1) Find the simple interest on £235 8s. 4d. in 3 years at 4 per cent. (2) Find the amount of £827 10s. in 7 years at 5 per cent. |