8. What is the interest of £563 at 6 per cent. per annum, for 126 days? Ans. £11 13s. 21d.+

num?

9. What is the interest of £560 for 60 days, at 5 per cent. per anAns. £4 12s. Old.+ 10. What is the interest of £364 18s. for 154 days, at 5 per cent. per annum? Ans. £7 13s. 111d.+ 11. What is the interest of £725 15s. for 74 days, at 4 per cent. per annum? Ans. £5 17s. 8d. + 12. What is the interest of £100 from the 1st. of June, 1851, to the 9th of March following, at 5 per cent. per annum?

Ans. £3 16 113d.+ RULE. prt+p=a.

II When p, r, t, are given to find a. 13. What will £279 12s. amount to in 7 years at 4 per cent. per annum ? 279-6X 045×7+279·6=£367·674. Ans. 14. What will £320 17s. amount to in 5 years, at 3 per cent. per annum? Ans. £376 19s. 11d. 2.8 qrs. 15. What will £679 138. amount to in 6 years, at 5 per cent. per annum ? Ans. £883 10s. 10d. 3.2 qrs. When odd time is given with the whole years, reduce it into days, and work with the decimal parts of a year which are equal to those days.

16. What will £926 12s. amount to in 5 years, at 4 per cent. per annum? Ans. £1130 9s. Od. 1.92 qrs. 17. What will £368 16s. amount to in 72 years, at 6 per cent. per annum? Ans. £554 11s. 7d. 3.68 qrs. 18. What will £273 18s. amount to in 4 years, 175 days, at 3 per cent. per annum ? Ans. £310 14s. 1d. 3.35080064 qrs.

III. When a, r, t, are given to find p. RULE.

α

tr+1=p.

19. What principal put to interest will amount to £367 13s. 5d. 3.04 qrs. in 7 years, at 4 per cent. per annum ?

045×7+1=1·315 then 367·674—1·315=£279 12s. Ans. 20. What principal will amount to £376 19s. 11d. 2.8 qrs., in 5 years, at 3 per cent. per annum ?

21. What principal will amount to £883 10s. years, at 5 per cent. per annum ?

22. What principal will amount to £1130 9s. years, at 4 per cent. per annum?

23. What principal will amount to £554 11s. years, at 6 per cent. per annum?

24. What principal will amount to £310 14s. in 4 years, 175 days, at 3 per cent. per annum?

IV. When a, p, t, are given to find r.

Ans. £320 17s 10d. 3.2 qrs. in 6

Ans. £679 13s. Od. 1.92 qrs., in 51

Ans. £926 12s. 7d. 3.68 qrs., in 7 Ans. £368 16s. 1d. 3.35080064 qrs. Ans. £273 18s.

RULE.

Pr. pt

25. At what rate per cent. will £279 12s. amount to £367 3s. 5d.

3.04 qrs. in 7 years?

367-674-279-6=88·074, and 279.6x7=1957.2; 1957.2=045 or 4 per cent. Ans.

then 88 074

26. At what rate per cent. will £320 17s. amount to £376 19s. 11d. 2.8 qrs. in 5 years ? Ans. 3 per cent.

27. At what rate per cent. will £679 13s. amount to £883 0s. 10d. 3.2 qrs. in 6 years? Ans. 5 per cent. 28. At what rate per cent. will £926 12s. amount to £1130 9s. Od. 1.92 qrs. in 5 years? Ans. 4 per cent. 29. At what rate per cent. will £368 16s. amount to £554 11s. 7d. 3.68 qrs. in 73 years? Ans. 6 per cent. 30. At what rate per cent. will £273 18s. amount to £310 14s. 1d. 3.35080064 qrs. in 4 years, 175 days?

Ans. 3 per cent.

V. When a, p, r, are given to find t.

a-p

RULE.

=t.

pr

31. In what time will £279 12s. amount to £367 13s. 5d. 3.04qrs. at 4 per cent? 367 674-279-6=88·074. 279.6×·045=12·5820; then 88 074-12.5820-7 years. Ans

32. In what time will £320 17s. amount to £376 19s. 11d. 2.8 qrs. at 3 per cent.? Ans. 5 years. 33. In what time will £679 13s. amount to £883 10s. 10d. 3.2 qrs. at 5 per cent.? Ans. 6 years.

34. In what time will £926 12s. amount to £1130 9s. Od. 1.92 qrs. at 4 per cent.? Ans. 5 years. 35. In what time will £368 16s. amount to £554 118. 7d. 3-68 qrs. at 6 per cent?

Ans. 7 years. 36. In what time will £273 18s. amount to £310 14s. 1d. 3-35080064 qrs. at 3 per cent. ? Ans. 4 years, 175 days.

ANNUITIES, OR PENSIONS &c., IN ARREARS.

Annuities or pensions, &c. 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.

NOTE. U represents the annuity, pension, or yearly rent; t, r, a, as before.

I. When u, r, t, are given to find a. RULE.

ttu-tu

2 -xr: +tu=a. 37. If a salary of £150 be forborne 5 years at 5 per cent.-what will it amount to?

5×5 x 150-5×150=3000, then

3000

2 -x05+5×150-£825 Ans.

38. If £250 yearly pension be forborne 7 years-what will it amount to in that time, at 6 per cent. P 39. There is a house let upon a lease of 5 years at £60 per annum Ans. £2065. -what will be the amount of the whole time at 4 per cent.?

40. Suppose an annual pension of £28 remain what would it amount to at 5 per cent. ?

unpaid for 8 yearsAns. £363 8s. 3d. Ans. £263 4s.

NOTE. When the annuities, &c., are 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, &c., and four times the number of years, and work as before.

41. If a salary of £150 payable every half-year, remains unpaid for 5 years-what would it amount to in that time at 5 per cent? Ans. £834 7s. 6d. 42. If a salary of £150 payable every quarter, was left unpaid for 5 years—what would it amount to in that time at 5 per cent.?

Ans. £839 1s. 3d. NOTE.-It may be observed, by comparing these last examples, that the amount of the half-yearly payments are more advantageous than he yearly, and the quarterly more than the half-yearly.

2a

II. When a, r, t, are given to find u. RULE. 43. If a salary amounted to £825 in 5 years, at 5 per cent-what was the salary?

825x2=1650, 5×5×·05-5×·05+5×2=11; then 1650-11=

£150 Ans. 44. If a house be let upon a lease for 5 years, and the amount for that time be £363 8s. 3d. at 41 per cent-what is the yearly rent?

45. If a pension amounted to £2065 in 7 years, at 6 what was the pension ?

46. Suppose the amount of a pension be £263 4s. in 8 per cent-what is the pension ?

Ans. £60. per cent Ans. £250 years, at 5 Ans. £28.

NOTE. When the payments are half-yearly, then take 4a, half of the ratio, and twice the number of years; and if quarterly, then take 8a, one-fourth of the ratio, and four times the number of years; and proceed as before.

47. If the amount of a salary, payable half-yearly, for 5 years, at 5 per cent. be £834 7s. 6d.—what is the salary?

Ans. £150.

48. If the amount of the annuity, payable quarterly, be £839 18. 3d. for 5 years, at 5 per cent.—what is the annuity?

III. When u, a, t, are given to find r. RULE.

Ans. £150.

2a-2ut

utt-ut

=r.

49. If a salary of £150 per annum amount to £825 in 5 yearswhat is the rate per cent?

825×2-150×5 × 2=150, then

cent. ?

150

150×5×5-150 × 5=.05

50. If a house be let upon a lease for 5 years, at £60 per annum, and the amount for that time be £363 8s. 3d.-what is the rate per Ans. 4 per cent. 51. If a pension of £250 per annum amounts to £2065 in 7 years-what is the rate per cent? Ans. 6 per cent. 52. If the amount of a yearly pension of £28 be £263 4s. in 8 years -what is the rate per cent.? Ans. 5 per cent.

NOTE. When the payments are half-yearly, take 4a-4ut for a dividend, and work with hair the annuity, and double the number of years for a divisor: if quar terly, take 8a-Sut, and work with a fourth of the annuity, and four times the num. ber of years.

53. If a salary of £150 per annum, payable half-yearly, amounts to £834 7s. 6d. in five years-what is the rate per cent.?

Ans. 5 per cent.

54. If an annuity of £150 per annum, payable quarterly, amounts to £839 18. 3d. in five years-what is the rate per cent.?

55. In what time will a salary of £150 per annum amount to £825, at 5 per cent.?

56. If a house be let upon lease for a certain time, for £60 per annum, and the amount be £363 8s. 3d., at 4 per cent.-what time was it let for? Ans. 5 years.

57. If a pension of £250 per annum, being forborne a certain time, amounts to £2065, at 6 per cent.-what was the time of forbearance? Ans. 7 years.

58. In what time will a yearly pension of £28 amount to £263 4s., at 5 per cent.? Ans. 8 years.

NOTE. If the payments are half-yearly, take half the ratio, and half of the annuity; if quarterly, one-fourth of the ratio, and one--fourth of the annuity; and t will be equal to those half-yearly or quarterly payments.

59. If an annuity of £150 per annum, payable half-yearly, amounts to £834 7s. 6d. at 5 per cent.-what time was the payment forborne? Ans. 5 years.

60. If a yearly pension of £150 payable quarterly, amounts to £839 18. 3d. at 5 per cent.-what was the time of forbearance? Ans. 5 years.

Present Worth of Annuities, &c., by Simple Interest. The examples under this head are left out, because they are entirely useless, erroneous, and absurd. More useful matter has been substituted.

1. What is the present worth of £357 10s. to be paid 9 months hence, at 5 per cent ?

357.5 75X 05+1

344.5783. Ans.

2. What is the present worth of £275 10s. due 7 months hence, at 5 per cent. ? Ans. £267 13s. 10-164d. 3. What is the present worth of £875 5s. 6d. due 5 months hence, at 4 per cent.? Ans. £859 3s. 3d. 3.2544 qrs.+ 4. How much ready money can I receive for a note of £75, due 15 months hence, at 5 per cent.? Ans. £70 11s. 9.1764d.+ RULE. ptr+p=s.

II. When p, t, r, are given to find s.

5. If the present worth of a sum of money, due 9 months hence, allowing 5 per cent. be £344 11s. 6d. 3.168 qrs.-what was the sum first due ? 344 5783 x 75 x 05+344-5783 £357 10s. Ans.

6. A person owing a certain sum, payable in 7 months, agrees to pay down £267 13s. 10-164d. allowing 5 per cent for present payment -what is the debt? Ans. £275 10s. 7. A person receives £859 3s. 3d. 3·2544 qrs. for a sum of money due in 5 months, allowing the debtor 41 per cent. for present payment -what was the sum due? Ans. £875 5s. 6d. 8. A person paid £70 11s. 9.1764d+. for a debt 15 months hence, he being allowed 5 per cent. for the discount-how much was the debt ?

III. When s, p, t, are given to find r. RULE.

Ans. £75.

=r.

tp

9. At what rate per cent. will £357 10s. payable 9 months hence, produce £344 11s. 6d. 3.168 qrs. for present payment?

10. At what rate per cent. will £275 108. payable 7 months hence, produce £267 13s. 10·164d. for present payment? Ans. 5 per cent. 11. At what rate per cent. will £875 5s. 6d. payable 5 months hence, produce the present pay ment of £859 3s. 3d. 3.2544 qrs. ?

Ans. 4 per cent.

12. At what rate per cent. will £75, payable in 15 months, produce the present payment of £70 11s. 9.1764d.+.?

IV. When s, p, r, are given to find t. RULE.

Ans. 5 per cent.

13. The present worth of £357 10s., due for a certain time to come, is £344 11s. 6d. 3.168 qrs., at 5 per cent.-in what time should the sum have been paid without any rebate?

14. The present worth of £275 10s., due for a certain time to come, is £267 13s. 10-164d., at 5 per cent.-in what time should the sum have been paid without any rebate?

Ans. 7 months.