Otherwise, Find the amount of 11. at compound interest for the given years less 1. Then find the sum of that progression, whose first term`is 1, and last term the said amount, and multiply the said sum by the given annuity. Example. Suppose an annuity of 3201. be 110 years in arrear, it is required to find what is now due, compound interest being allowed on every payment, at 5 First Method. 320. .05)201.247040 annum? cent. 2. An annuity of 201. annum is forborne 7 years, what is then due at 6 cent. compound interest? Answ. 1671. 17s. 6d. 3. If 301. annum, yearly rent be forborne 9 years; what will it amount to at 6 cent. annum compound interest? Answ. 3441. 14s. 94d. 4. Suppose a person who had an annuity of 201. suffered it to be in arrear for 15 years, what had he then to receive; compound interest being computed at 6 Pannum? Answ. 4651. 10s. 41⁄2d. SECT. III. Of Rebate at Compound Interest. Rule. cent. Find the amount of 11. for the given time at the given rate, and divide the given sum to be rebated thereby, the quotient will be the sum to be paid down. Examples. Examples. What ready money ought to be paid down for a debt of 6291. 17s. 1 d. due 3 years hence, discount at 8 ceat. annum, compound interest. 1.259712) 629.856000(5001. Answ. 6298560 2. Suppose 5211, 4s. 111d, were to fall due 10 years hence, how much ought to be paid now in full satisfact oa for it, discount being allowed at 5 compound interest? Answ. 3201. cent. annum, 3. A legacy of 520. 18s. 7 d. is left to be paid in 4 year's time; but the Executor is willing to pay it at the expiration of 1 year, upon being allowed discount at compound interest at 5 cent. which being agreed to, what must he pay? Answ. 4501. SECT. IV. Of the present, Worth of Annuities; and of Leases in Reversion. Rule. Find the present worth of the first and last year's annuity, which are the greatest and least terms of a geometrical progression: Then find the sum of that progression. 1. What is 301 yearly rent to continue 7 years, worth in ready money, allowing 6 cent. compound interest, to the purchaser? 30 1.06 =28.3019 worth of the first year's ann, and comp. [teria. 30 19.9517 the last and least term. 1.50363 .06)1 3502 139.17 28.3019 167.4719 Answ. £.167 9 5 2. There is an annuity of 201. annum, to continue 7 years to be sold for ready money: What is it worth compound compound interest being allowed the purchaser at 5 d cent.? Answ. 1151. 14s. 6d. 3. An annual rent of 3651. paid yearly, and to continue 12 years, is to be sold for ready money; what is it worth at 5 cent, compound interest? Answ. 32351. Is. 9d. Now to find the value of an annuity or lease in revers sion, this is the Rule. Find the present worth of the annuity as commencing immediately, and then find what ready money ought to be paid for that sum, rebate at compound interest being allowed for the term of years till the commencement of the annuity or lease. Suppose it were required to compute the present worth of 751. yearly rent, which is not to commence until 10 years hence, and then to continue 7 years after that time, at 6 cent. compound interest. 1. An annuity of 751. dannum, to continue 7 years. may be found at 6 cent, compound interest to be worth 4181. 19s. 63d. 2. Then we are to find how much ready money ought to be paid for this sum as due 10 years hence,' which will be found 2331. 15s. 9d. the answer required. An annuity of 241. annum, to begin 7 years hence, and to continue 21 years; what is it worth, allowing the purchaser 6 cent. compound interest? Answ. 2691. 10s. Sd. But as the finding the compound interest of any sum is troublesome, for a large term of years; the following Tables will make the work of questions relating to compound interest very easy. 14.205787 14.971643 12 15.917126 16.869940 13 17.712982 18.182137 14 19.598631 21.015065 15 21.578563| 23.275969 16 23.657491| 25.672527 17 25.840366 28.212879 18 28.132384 30.905651 19 30.539009| 33.759992 20 33.065954 36.785590 21 35.719251 39.992727 22 38.505214 43.392291 241,430475 46.995826 244.501999 50.815575 25 47.727099. 54.864510 26 51.113453 59.156381 254.669126 63.705763 28 58.402585 68.528112 29 62 392712 73.639799 CONSTRUCTION AND USE OF THESE TABLES. The first Table may be constructed as shewn p. 308,309. The second may be constructed from the first, thus, Let I be divided by 4.538039 the last number of the first, and the quotient .220359 is the last number of the second. But the terms of the second Table are a decreasing geometrical progression, whose ratio is 1.05,1.06; so contrarywise the progression beginning at the last term and continued to the first will be an increasing progression, and therefore the last term being found as above, the rest may be found from it. 31 |