CASE 3. Q. When U, P, and T, are given to find R, how is it discovered? 2ut-2p A. Thus: 2p-ut tut EXAMPLES: 1 I demand at what rate per cent will the yearly rent of 501 to continue 6 years, produce the present worth of 2591 12s 3d 2 qrs. Ans. 51 per cent. 2 If the yearly rent of 80l per annum to continue 5 years, being 344/ 12s 3d 2 qrs. present worth, what is the rate per cent? Ans. 61 cent. per 3. If a salary of 401 per ann. to continue 7 years, produce 245/ for the present worth, what is the rate per cent ? Ans. 71 per cent. 4 If a pension of 30l per annum to continue 5 years, produce 1331 9s 4d 2 qrs. for the present worth, what is the rate per cent? Ans. 411 per cent. Note. When the Annuities or Rents are to be paid half-yearly or quarterly, then, For half-yearly payments take half of the Annuity or yearly Rent, and twice the Number of Years, that is, reduce the Years into half years, and then the Quotient of the upper part divided by the lower, will be the ratio of half the Rate per Cent. But, For quarterly payments, take a fourth part of the Annuity or yearly Rent, and four times the Number of Years; that is, reduce the Years into quarters; and then the quotient of the upper Part divided by the.. lower will be the Ratio of a 4th part of the Rate per Cent. 5 If a lease of a house of 50l. per ann. payable halfyearly, having 6 years to come, is sold for 262l. 10s. I de mand the rate per cent? Ans. 56 per cent. 6 A lease of a house of 50l per ann. payable quarterly having 6 years to come, is sold for 2631 18s 9d 3 qrs. I demand the rate per cent? Ans. 51 per cent. CASE 4. Q. When U, P, and R, are given to find T, how is it discovered? A. Thus: first 2 2p EXAMPLES. 1 If 501 yearly rent produce the present worth of 259/ 12s 3d 2 qrs. at 5 per cent what is the time of its continuance? Answer 6 years. 2 I demand how long 801 per annum may be purchased for 3441 12s 3d 2 qrs at 6 per cent? Answer 5 years. 3 How long must a salary of 40 per annum be enjoyed for 2451 at 4 per cent? Ans. 7 years. 4 What time may a pension of 301 per ann. be bought for 1331 9s 4d 2 qrs. at 4 per cent? Answer 5 years. Note. 1 If the payments are to be half yearly, then U will be half of the given lease, pension, &c. and R will be-half of the Ratio of the given rate, and T which is required, will be=the number of payments or half years. 2 If the payments are to be quarterly, then U will be a fourth part of the given Lease, Pension, &c. and R will be—a fourth part of the ratio of the given rate, and T will be the number of quarterly pay ments. 5 A lease of an house of 50l per annum payable halfyearly is sold for 2621 10s at 5 per cent. I demand the number of payments and the time to come? Ans. 12 payments 6 years. 6 A lease of an house of 501 per annum payable quarterly, is sold for 2631 18s 9d 3qrs. at 5 per cent. I demand the number of payments, and the time to come.? Ans. 24 payments, 6 years. Of Annuities, Leases, &c. taken in Reversion. Q. How do you find the present worth of an annuity &c. in reversion? A. Thus; first find the present worth of the yearly. sum at the given rate, and for the time of its continuance: to do which, there are given U, T, and R, to find P, which is thus discovered: Secondly, find what principal being put to interest will amount to P, at the same rate, and for the time to come before the annuity, &c. commences; and that will be the present worth of the annuity, &e. in Reversion: therefore fet P be changed into A=the amount, and then there will be given A, R. and T, to find P, or the principal which is thus discovered: α EXAMPLES. 1 What is the present worth of a lease of 30% per ann. to continue 3 years, but is not to commence till the end of 2 years, allowing 4 per cent to the purchaser? Ans. 771 7s 7.2d. 2 I have the promise of a pension of 177 per ann. for 7 years, but it does not commence till the end of 4 years, and I am willing to dispose of the same for the present payment at the rate of 5 per cent-I demand the present worth? Ans. 84/ 9s 6d. 3 There is a legacy of 201 per ann. for 8 years, left to a person of 16 years of age; the time of payment is to commence at the year of perfection, i. e. at 21 years; but he wanting a sum of money, is minded to sell the same at 4 per cent-I demand the present worth? Ans. 115 3s od 1.44 qr. 4 A good natured gentleman being minded to bestow a favour upon an unthankful wretch, settled upon him an income of 351 per ann. for 12 years, to commence five years after such settlement; but he wanting money to follow his extravagances, sold it at the rate of 10 per cent.I demand how much he received for the present worth? Ans. 1977 5s 5d 1.696 qr. CASE 5. Q. How do you find the yearly income of an annuity, &c. in Reversion? A. Thus: First, find the amount of the present worth of the yearly sum, at the given rate, and for the time before the reversion: to do which, there are given P, T, and R, to find A, which is thus discovered: ptr+p=a Secondly, Find what yearly rent being sold will produce A, for the present worth, at the same rate and for the time of its continuance: and that will be the yearly sum required: therefore change A into P, and then there will be given P, R, and T, to find U, or the yearly sum, thus: rt+1. rtt-rt+2t. EXAMPLES. 1 There is a lease of a house taken for 3 years, but commences not till the end of 2 years: and the lesseewould sell the time for 761 7s 7.2d present payment, allowing 4 per cent to the purchaser: I demand the yearly rent P Ans. 30l per ann. 2 I have the promise of a pension for 7 years, which will not commence till the end of 4 years; and I have disposed of the same for the present payment of 841 9s 5d. allowing 5 per cent to the purchaser; I demand the yearly income? Ans. 171. 3 There is a legacy of a certain rate per ann. for 8 years left to a person of 16 years of age; but the time of payment must not commence till the age of perfection; and the same person wanting a sum of money, sold it for 115/ 38. od allowing 4 per cent to the buyer: I demand the yearly rate? Ans. 201. 4 A good natured gentleman being minded to bestow a favour upon an unthankful wretch, settled an income upon him for 12 years, at a certain rate per annum, to commence 5 years after such settlement; but he wanting money to follow his extravagance, sold it for 1977 5s 5d 2qrs. allowing 10 per cent to the buyer for the present payment; I demand the yearly value? Ans. 351. OF SIMPLE INTEREST FOR DAYS. Q. How do you find the Simple Interest of any sum of Money for any number of days? A. Multiply the interest of one pound for one day, at the given rate, by the principal, and by the number of days; the last product is the interest required. Note. The Interest of one Pound, for one day at 1 What is the interest of 120l för 126 days, at-4 per cent? Ans. 17 13s id 2 qrs+.. 2 What is the interest of 126l för 145 days, at 6 per cent? Ans. 31 Os od 3 qrs+. 3 What is the interest of 1007 from the first of June, 1796, to the 8th of March following, at 5 per cent? Ans 8/10s-11d 3 grs. 4 What is the interest of 2001 from the 14th of August 1781 to the 19th of December following, at 6 per cent? Ans. 4 4s id 3qrs.+ 5 What is the interest of 10l for 25 days at 5 per cent? Ans. 8d.+ 6 What is the interest of 401 for 40 days, at 4 per cent? Ans. 38 6d.+ Note. There is another way of answering Questions in interest for Days, which is laid down in Case 1, in Simple Interest, page 62. as appears by the 8th Question in that Case. The reader may use which he likes best, or both if he pleases. OF REBATE OR DISCOUNT. Q. What particular letters are used in Rebate? S, the sum to be discounted. P, the present worth of that sum due at any time to come. F, the time before it becomes due. R, the Ratio, or the rate per cent. CASE 1. Q. When S, T, and R, are given to find P, how is it discovered? What is the present worth of 795 11s 2d for 1] months, at 6 per cent? Ans. 7541 is 8d.-+ 2 What is the present worth of 1617 10s for 19 months at 5 per cent? Ans. 1491 13s od 3 qrs.+ 3 If a legacy of 1000l is left me the 24th of July, 1781, to be paid on the Christmas-Day following, what must I receive when I allow 6 per cent for present payment? Ans. 9751 3s od 3 qrs.+. CASE 2. Q. When P, T, and R, are given to find S, how is it discovered? A. Thus; ptr+p=s. EXAMPLES. 1. Suppose I receive 754/ 18 8d now, for a sum of money, due 11 months hence, allowing per cent for present payment: I demand the sum that was due at first? Ans. 795l 11s 2d. 2 There is a certain debt payable 19 months hence; but I agree with the debtor to pay me down 1497 12s odą |