(2) What is the Interest of 500/ from May the 12th, 1784, to November the 24th, 1789, at 33 per Cent. per Ann? Case 2. When the Interest required is for Days only. RULE. Multiply the Interest of 1/ for one Day, at the given Rate, by the Principal and Number of Days; it will give the An swer. The Interest of 17 for one Day is thus found, Viz. As 365 : ,05 : : 1,0001369863, &c. (3) What is the Interest of 370/ 10s for 220 Days, at41 per Cent per Annum ? (4) What is the Interest of 600/ from the 1st of July, 1789, to the 24th of February following, at 6 per Cent. ? Case 3. When the Principal, Time, and Rate per Çént. are given, to find the Amount. RULE. Find the Interest by Theorem 1, which, added to the Principal, will give the Amount. Thus, THEOREM 2. ptr + p A. EXAMPLES. (5) What will 284/ 10s amount to in 7 Years, at 31 per Cent. per Annum ? (6) What will 6721 5s amount to in 5 Years, at 4 per Cent. per Annum ? (7) What will 500/ amount to in 6 Years 120 Days, at 4 per Cent. per Annum? Case 4. When the Rate, Time, and Interest are given, to find the Principal. RULE. Divide the Interest by the Product of Rate and Time, the Quote is the Principal. (8) I demand what Principal, being put to Interest for 3 Years, will gain 69/ 13s 6d. at 5 per Cent. per Annum? (9) I demand what Principal, being put to Interest for 51 Years, will gain 647 7s at 44 per Cent. per Annum? (10) I demand what Principal, being put to Interest for 4 Years, at 4 per Cent. will gain 677/ 15s 93d. ? Case 5. When the Amount, Rate, and Time are given, to find the Principal. RULE. Add 1 to the Product of the Rate and Time, and by that Sum divide the Amount: the Quote is the Principal. Thus, THEOREM 4. a tr + 1 EXAMPLES. (11) What Principal, being put to Interest, will amount to 354 4s 0d in 7 Years, at 34 per Cent. per Annum ? (12) What Principal, being put to Interest, will amount to 500/ 9s 34d. in 6 Years 5 Months, at 5 per Cent. per Annum? (13) What Principal, being put to Interest for 7 Years 220 Days, at 44 per Cent. per Annum, will amount to 100% ? Case 6. When the Principal, Interest, and Rate are given, to find the Time. RULE. Divide the Interest by the Product of the Principal and Rate: the Quote is the Time. Thus, THEOREM 5. I EXAMPLES. (14) In what Time will 464/ 10s gain 691 13s 6d at 5 per Cent. per Annum ? (15) In what Time will 2607 gain 647 7s at 4 per Cent. per Annum ? (16) În what Time will 500/ gain 130/ 9s 7d at 61⁄2 per Cent. per Annum ? Case 7. When the Principal, Interest, and Rate are given, to find the Time. RULE. Divide the Amount, less the Principal, by the Product of the Principal and Rate: the Quote is the Time. (17) In what Time will 284/ 10s amount to 354/ 4s 0dat 34 per Cent. per Annum ? (18) In what Time will 672/ 5s amount to 847/ 17s 6d. at 42 per Cent. per Annum ? (19) In what Time will 378/ 18s amount to 500/ 9s 3 d. at 5 per Cent. per Annum ? Case 8. When the Principal, Interest, and Time are given, RULE. Divide the Interest by the Product of the Principal and Time: the Quote is the Rate. (20) At what Rate per Cent. will 464/ 10s gain 69/ 13s 6d in 3 Years? (21) At what Rate per Cent. will 2601 gain 641 7s in 51 Years? (22) At what Rate per Cent. will 5607 12s 83d gain 235/ 9s 4d in 7 Years? Case 9. When the Principal, Amount, and Time are given, to find the Rate. RULE. Take the Difference between the Amount and Principal, and divide it by the Product of the Principal and Time: the Quote is the Rate. Thus, THEOREM 8.4 r. pt EXAMPLES. (23) At What Rate per Cent. will 284/ 10s amount to 354/ 4s 0d in 7 Years? (24) At what Rate per Cent. will 378/ 18s amount to 500! 9s 34d in 6 Years? (25) At what Rate per Cent. will 6721 5s amount to 847/ 17s 6d in 54 Years? LXII. ÓF ANNUITIES, PENSIONS, &c. in ARREARS, at SIMPLE INTEREST. AN Annuity is a Yearly Income arising from Money, &c. and is either paid for a Term of Years, or upon a Life. Annuities or Pensions are said to be in Arrears, when they are payable or due either Yearly, Half-Yearly, or Quarterly, and are unpaid for any Number of Payments. Here U represents the Annuity, Pension, or Yearly Reat, A, T, R, as before. Case 10. When U, R, T, are given, to find A. When the Annuity, &c. is to be paid Half-Yearly, or Quarterly, then for Half-Yearly Payments take Half the Ratio, Half the Annuity, &c. and twice the Number of Years; and for Quarterly Payments take a fourth Part of the Ratio, a fourth Part of the Annuity, and four Times the Number of Years; which work with as per Theorem. EXAMPLES. 26) If 250 Yearly Rent, Pension, &c. be forborne or unpaid 6 Years, what will it amount to in that Time, at 3 per Cent. for each Payment, as it becomes due? (27) If a Salary of 250/ payable every Half-Year, remain unpaid for 6 Years, what would it amount to in that Time, at 3 per Cent. per Annum? (28) If a Salary of 250/ payable every Quarter, was left unpaid for 6 Years, what would it amount to in that Time, at 3 per Cent. per Annum ? It may be observed, by comparing the Answers of the three last Examples, that the Half-Yearly Payment is more advantageous than the Yearly one, and also the Quarterly more than the Half-Yearly. Case 11. When A, R, and T, are given, to find U. When the Payments are Half-Yearly, take 4a; if Quarterly, 8a; and proceed with the Ratio and Time as before. |