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5 k demand what principal will amount to 8711 3s od 2.4 qrs. in 10 years, at 41 per cent. per ann. ? Ans. 6001 14s.

6 I demand what principal will amount to 47001 in 5 years, at 3 per cent. per aun. ?

Ans. 40001 7 I demand what principal will amount to 328l 5s 2d 3.38 qrs. in 3 years and 148 days, at 5 per cent ? Answer 280l !0s

8 What principal being put to interest for 189 days, at 4 per cent will amount to 2001 1s 2d;

Ans. 196. CASE 3. Q. When A. P, and T are given to find R, how is it discovered ? A. Thus: amp

tp.

EXAMPLES. 1 At what rate per cent will 6671 10s amount to 8731 19s. in 9 years ?

Ans. 61 per cent. 2 At what rate per cent will 5081 14s amount to 5341 2s 8d 1.6 qr. in one year

?

Ans. 5 per cent. 3 At what rate per cent will 72001 amount to 95401 in 64 years?

Ans. 51 per cent. 4 At what rate per cent will 1110l 18s amount to 18191 Is 11d 2.8qrs. in 12 years ?

Ans. 57 per cent. 5 At what rate per cent will 6001 14s amount to 871106 3d 2.4 qrs. in 10 years ?

Ans. 4; per cent. 6 At what rate per cent will 40001 amount to 47001 in 5 years?

Ans. 3} per cent. 7 At what rate per cent will 2801 10s amount to 3281 55 2d 3.38 qrs. in 3 years and 148 days? Ans. 51 per cent.

8 At what rate per cent will 1961 amount to 200l 1$ 2d1 in 180 days?

Ans. 41

CASE 4. Q. When A, P, and R, are given to find T, how is it discovered ? A. Thus : QP

per cent,

I

rp EXAMPLES.

i In what time will 5671 10s amount to 8737 195 at 6

per cent?

Ans. 9 years

2 In what time will 5081 14s amount to 5341 Os 8d 1.6

Ans. 1 year. qr. at 5 per cent? 3 Io what time will 72001 amount to 9540 at 5 per cent.

Ans: 6 gears.

Ans. 10 years.

Ans. 5 years.

per cent?

4. In what time will 11101. 18s. amount to 18191. 1's. 11d. 2. Sqrs. at 5 per cent?

Ans. 12 years. 5. In what time will 600l. 14s. amount to 8711. Os. 3d. 2. 4qrs. at 4 per cent?

6. In what time will 40001. amount to 47001. at 3} per cent?

7. In what time will 2801. 10s, amount to 3281, 55. 2d. 3. 58qrs. at 5 per cent? Ans. 3 years 148 days. 8. In what time will 1961. amount to 2001. Is. 2d at 4

Ans. 189 days. 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. N, T, and A, as before.

OASE 1. Q. When U, R, and T, are given to find A, how is it discovered ? A. Thus ; tut-11

-Xr: tutto

2

EXAMPLES. 1. If an annuity of 701. 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 onnitted for 7 years, what will be the amount in that time at 6l. 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 50l 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 1001 per ann. be forborne 7 years, what is the amount at 4, per cent?

Ans. 794) 1os. 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 diways half of the ratio, ha!f 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 amornt to in that time at 5 per cent? Ans. 3891 78 6d.

6. If 701 annuity, payable every quarter, were unpaid 5 years, what will it amount to in that time at 5 per certy Alls. 3911 11s 3d.

0

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?

A. Thus: 2a

trt-tr + 2t

EXAMPLES.

*l. If the amount of an annuity for 5 years at 5 per cent be 3851 what is the annuity? Ans. 701.

2. If the amount of a pension be 4621 118 2d 1.6qr. the time be 7 years, and the rate per cent 6l what is the per-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? Aps. 50.

4. If a salary amounts to 7942 108 in 7 years, at 4 per cent what is the salary? Ans. 1001 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 78 6d, what is the annuity ? Answer, 701.

6. If the amount of an annuity, payable quarterly, for 5 years, at 5 per cent be 3911 11s 3d. what is the annuity? Answer, 701.

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

A. Thus: 20-2ut

uttut

EXAMPLES.

1. If an amuity of 70l per ann. amounts to 3851 in 5 years; 1 demand ihe rate per cent? Ans. 51.

2. If a pension of 56l per ann. amount to 4621 118 2d 1.6qr. in 7 years, what is the rate

per

cent? Ans. 61. 3. If a house be let upon lease for 7 years at 50l per ann, and the amount for that time be 3921. what is The cent? Answer,

41 4. If a salary of 100l per annum being forborne 7 years amounts to 79 41 10$, I demapd the rate per cent? Ans. 46

rate per

per cent.

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

5. If an annuity of 701 per ann. payable half yearly, being forborne 5 years, amounts to 3891 78 6d. I demand the rate per cent? Ans. 5l per cent.,

6. If an annuity of '70l per annum payable quarterly, amounts to 39 11 118 3d in 5 years; 1 demand the rate per eent? Answer, 51

CASE 4. Q. When U, A, and R, are given to find T, how is it discovered ? A. Thus, First 2

13

per cent.

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EXAMPLES:

Ans. 7 years.

1. In what time will 70l per annum amount to 3851 for: borne at 5 per cent? Answer 5 years.

2. In what tine will a pension of 561 per ann. amount to 4621 11s 2d 1.6qr. at 6 per cent?

3. If a house he let upon lease, for a certain time, for 501 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 certain time, amounts to 7941-10s at 45 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 qudr. terly; then T' will be equal to the number of quarterly payments.

5. If an annuity of 70l per ann. payable half-yearly, being forborne, amounts to 3891 78 6d at 5 per cent; I demand the time and payment forborne ? Answer, 10 pay. ments=5 years.

6. If an annuity of 702 per annum payable quarterly, being forborne, amounts to 3911 118 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?

Thus; rt-rt X2t

tu=p. 2rt+2

EXAMPLES. 1. What is the present worth of 50l per ann. to conţinue 6 years at 5 per cent? Ans. 2590 12s 3d 2.4+qrs.

2. What is 80l yearly rent, to continue 5 years, worth in ready money, at 6 per cent? Ans. 2441 13s 3d 5+2qrs.

3. What is a salary of 40l 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 45 per cent ?. Ans. 1381 98 4d 2.6+qrs.

Note. Observe the same node here, which is given in Case 1, in An. nuities and Pensions in arrears, concerning half-yearly and quarterly payments.

5. What is the present worth of 50l per ann. payable balf-yearly for 6 years, at 5 per cent? Ans. 2621 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 i& more advaritageous 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. Thus; rt+1

-G9p=4. rt-rt+2t 1. There is a lease of a house

years to come; I demand the yearly rent, when the present worth at 5 per cent is 2591 12s 3d 2.4qrs? Answer, 501

2. What yearly rent is that, the present worth of which for 5 years is 344l 128 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 245l for the present worth? Ans. 401.

4. If the present worth of a pension to continue 5 years at 4's per cent be 1331.98 40 , I demand the pension ? A.801.

Note. When the payments to be made are half-yearly, you must mulu tiply 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 presept wurth at 5 per cent is 2621 10s. Ans. 501.

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. 50%

EXAMPLES.

per ann.

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