5 I demand what principal will amount to 8711 3s O₫ 2.4 qrs. in 10 years, at 4 per cent. per ann. ? Ans. 600l 14s. 6 I demand what principal will amount to 4700l in 5 years, at 31 per cent. per aun. ? Ans. 4000/

7 I demand what principal will amount to 3287 5s 2d 3.38 qrs. in 3 years and 148 days, at 5 per cent? Answer 2801 ros

8 What principal being put to interest for 189 days, at 4 per cent will amount to 2001 1s 2d4 Ans. 196.

CASE 3.

Q. When A. P, and T are given to find R, how is it discovered? A. Thus: a-p

tp.

EXAMPLES.

1 At what rate per cent will 667/ 10s amount to 8731 19s.

in 9 years?

2 At what rate per cent will 5087 14s 8d 1.6 qr. in one year

3 At what rate per cent will 7200l 61 years?

4 At what rate per cent will 1110 1s 1id 2.8qrs. in 123 years ?

5 At what rate per cent will 600l 3d 2.4 qrs. in 10 years?

6 At what rate per cent will 4000l years ?

Ans. 61 per cent. amount to 5341 25 Ans. 5 per cent. amount to 9540l in Ans. 51 per cent. 18s amount to 1819/ Ans. 5 per cent. 14s amount to 871/08 Ans. 4 per cent. amount to 4700l in 5 Ans. 3 per cent.

7 At what rate per cent will 2807 10s amount to 3281 5s 2d 3.38 qrs. in 3 years and 148 days?

Ans. 51 per cent.

8 At what rate per cent will 1967 amount to 2001 18 2d4 in 180 days? Ans. 41 per cent.

CASE 4.

Q. When A, P, and R, are given to find T, how is it discovered? A. Thus a-p

=T..

rp.

per cent?

EXAMPLES.

1 In what time will 5671 10s amount to 8737 19s at 6 Ans. 9 years 2 In what time will 508/ 14s amount to 534/ 2s 8d 1.6 qr. at 5 per cent? Ans. 1 year. 3 In what time will 72007 amount to 9540 at 5 per cent.

Ans. 64 years.

4. In what time will 11101. 18s. amount to 18197. 1s. 11d. 2. 8qrs. at 5 per cent? Ans. 12 years. 5. In what time will 600l. 14s. amount to 8711. Os. 3d. 2. 4qrs. at 41 per cent? Ans. 10 years.

6. In what time will 4000l. amount to 4700l. at 34 per cent? Ans. 5 years.

7. In what time will 2801. 10s. amount to 3281. 5s. 2d. 3. 58qrs. at 5 per cent ? Ans. 3 years 148 days. 8. In what time will 1967. amount to 2001. 1s. 24d at 4 Ans. 189 days. per cent?

OF ANNUITIES OR PENSIONS IN ARREARS.

Q. What is meant by annuities or pensions in arrears ? A. Annuities or pensions are said to be in arrears, when they are payable, either yearly, half yearly, or quarterly, and are unpaid for any number of payments. Note. U represents the annuity pension, &c. R, T, and A, as before.

CASE 1.

Q. When U, R, and T, are given to find A, how is it discovered? A. Thus; tut-tu

-Xr: tut += 2 EXAMPLES.

1. If an annuity of 70l. be forborne 5 years, what will it amount to in that time, at 5 per cent? Ans. 3851.

2. If the payment of a pension be omitted for 7 years, what will be the amount in that time at 61. per cent when the pension is 561. per ann? Ans. 4621. 11s. 2d. 1.6qr.

3. A house is let upon lease for 7 years, at 50% per ann. I demand the amount for that time at 41 per cent for the forbearance of payment? Ans. 3921.

4. Suppose a salary of 100l per ann. be forborne 7 years, what is the amount at 41 per cent? Ans. 7941 10s.

Note. When the annuities or rents are to be paid by half yearly or quarterly payments, as most generally they are, then,

For half-yearly payments, take always half of the ratio, half of the yearly rent, and twice the number of years—that is, reduce the years into half-years for R,U, and T-But

For quarterly payments, take a fourth part of the ratio, a fourth part of the yearly rent, and four times the number of years, that is, reduce the years into quarters, and work as before.

5. If 70l annuity, payable every half year, were unpaid 5 years, what will it amount to in that time at 5 per cent? Ans. 3897 7s 6d.

6. If 70l annuity, payable every quarter, were unpaid 5 years, what will it amount to in that time at 5 per cent Ans. 391 11s 3d.

Note. By comparing these two examples with the first it may be observed, that the amount of half-yearly payments is more advantageous than yearly payments, and quarterly than half-yearly payments.

CASE 2.

Q. When A, R and T, are given to find U, how is it discovered?

EXAMPLES.

1. If the amount of an annuity for 5 years at 5 per cent be 3851 what is the annuity? Ans. 70l.

2. If the amount of a pension be 462 11s 2d 1.6qr. the time be 7 years, and the rate per cent 67 what is the pen-sion? Ans. 561.

3. If a house be let upon lease for 7 years, and the amount for that time be 3921 at 4 per cent. what is the yearly rent? Ans. 50%.

4. If a salary amounts to 7941 10s in 7 years, at 41 per cent what is the salary? Ans. 100% per ann.

Note. When the payments are half-yearly, 4a must be divided, when they are quarterly, 8a must be divided as before.

5. If the amount of an annuity, payable half-yearly, for 5 years, at 5 per cent be 3891 7s 6d, what is the annuity? Answer, 701.

6. If the amount of an annuity, payable quarterly, for cent be 3911 11s 3d. what is the annuity? 5 years, at 5 per

Answer, 701.

CASE S.

Q. When U, A, and T, are given to find R, how is it discovered?

A. Thus: 2a-2ut

utt-ut

EXAMPLES.

Ans. 61.

1. If an annuity of 70l per ann. amounts to 3851 in 5 years; I demand the rate per cent? Ans. 51. 2. If a pension of 561 per ann. amount to 4627 118 2d 1.6qr. in 7 years, what is the rate per cent ? 3. If a house be let upon lease for 7 years ann, and the amount for that time be 3921. rate per cent? Answer, 41 per cent.

at 50% per what is the

4. If a salary of 100 per annum being forborne 7 years amounts to 7941 108, I demand the rate per cent? Ans. 41.

Note. When the payments are half-yearly, then 4a-8ut must be divided; but when they are quarterly, then 8a-8ut must be divided as before.

5. If an annuity of 70l per ann. payable half yearly, being forborne 5 years, amounts to 3891 7s 6d. I demand the rate per cent? Ans: 5 per cent.

6. If an annuity of 70l per annum payable quarterly, amounts to 391 118 3d in 5 years; 1 demand the rate per cent? Answer, 51 per cent.

CASE 4.

Q. When U, A, and R, are given to find T, how is it discovered?

1. In what time will 70 per annum amount to 3851 forBorne at 5 per cent? Answer 5 years.

2. In what time will a pension of 561 per ann. amount to 462/ 11s 2d 1.6qr. at 6 per cent? Ans. 7 years.

3. If a house be let upon lease, for a certain time, for 50% per annum, and the amount be 3921 at 4 per cent; I demand the time that it was let for? Ans. 7 years.

4. If a salary of 100l per annum being forborne a cer tain time, amounts to 794/ 10s at 44 per cent; I demand the time of forbearance? Answer, 7 years.

Note. If the payments were half-yearly, then T will be equal to the number of half years, or payments; but if they were to be made quar. terly, then Twill be equal to the number of quarterly payments.

5. If an annuity of 70l per ann. payable half-yearly, being forborne, amounts to 3891 7s 6d at 5 per cent; I demand the time and payment forborne ? Answer, 10 payments 5 years.

6. If an annuity of 70l per annum payable quarterly, being forborne, amounts to 3911 11s 3d at 5 per cent; I demand the time and payments forborne? Answer, 20 pay. ments=5 years.

Of the Present Worth of Annuities, or Pensions, etc. Note. Prepresents the present worth-U, T and R, as in the last. CASE 1.

Q. When U, T and R, are given to find P, how is it discovered?

1. What is the present worth of 50l per ann. to continue 6 years at 5 per cent? Ans. 2591 12s 3d 2.4+qrs. 2. What is 801 yearly rent, to continue 5 years, worth in ready money, at 6 per cent? Ans. 2441 12s 3d 5+2qrs. 3. What is a salary of 401 per ann. to continue 7 years, worth in ready money, at 4 per cent. Ans. 2451.

4. What is a pension of 301 per ann. for 5 years worth in ready money, at 44 per cent? Ans. 1387 98 4d 2.6+qrs. Note. Observe the same note here, which is given in Case 1, in Annuities and Pensions in arrears, concerning half-yearly and quarterly payments.

5. What is the present worth of 501 per ann. payable half-yearly for 6 years, at 5 per cent? Ans. 262/ 10s.

6. What is the present worth of 50l per anu. payable quarterly for 6 years, at 5 per cent. Ans. 2681 188 9d3.6qrs.

Note. By comparing these two examples with the first, it may be observed, that the present worth of half-yearly payments is more advantageous than yearly payments, and the present worth of quarterly than half-yearly payments.

Q. When P, T, and R, are given to find U, how is it discovered?

1. There is a lease of a house 6 years to come; I demand the yearly rent, when the present worth at 5 per cent is 259/ 128 3d 2.4qrs? Answer, 50l per ann.

2. What yearly rent is that, the present worth of which for 5 years is 344l 12s 2d 2qrs. at 6 per cent? Answer, 801 per annum.

3. What salary is that which for 7 years continuance at 4 per cent produces 245/ for the present worth? Ans. 40l. 4. If the present worth of a pension to continue 5 years at 4 per cent be 1337.98 4d 3, I demand the pension? A.801. Note. When the payments to be made are half-yearly, you must multiply by 4p, but when they are quarterly, then multiply by 8p to find u. 5. There is a lease of a house, payable half yearly, for six years to come, I demand the yearly rent, when the present worth at 5 per cent is 2621 10s. Ans. 50l.

6. There is a lease of a house, payable quarterly, for 6 years to come, I demand the yearly rent, when the present worth at 5 per cent is 5631 13s 9d 3.6qrs. Ans. 5Qk