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OF SIMPLE INTEREST.

What particular Letters are used here?

Q.

A. These : P, any Principal.

T, the time.
R, the ratio of the rate per cent.

A, the Amount.
Q. What is the ratio ?

A. It signifies only the simple interest of 11 for one year, at any proposed rate of interest per cent, and is thus found,

100 : 6 :: 1 : 0.06

100 : 5 :: 1 : 0.05

A TABLE OF RATIONS.
Rate per Ct. Ratio. (Rate per Ct. Ratio.

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CASE 2. Q. When P, T and R are given to find A, how is it discovered ?

A. Thus ptr +p=A.

Note. Any quantity of Letters put together like a word, denote continual Multiplication.

EXAMPLES. 1. What sum will 5671 108 amount to in 9 years, at 6 per cent per annum ?

Ans. 8731, 198. 2. What will 5081 148. amount to in 1 year at 5 per cent. per annum ?

Ans. 5341 2s 8d 1. 6

qrs. 3. What will 600l 14s. amount to in 10 years, at 4 per cent. per annum?

Ans. 8711 os. 3d. 2.4.qrs. 4. What will 40001, amount to in 5 years, at 3 per cent. per annum ?

Ans. +7001. Note. When the time given does not consist of whole years, then reduce the odd time into Decimal parts of a year. And unless such parts of a year chance to be 1-10 of a year, the best way will be to reduce the odd times into days, and then work with the Decimal parts of a year, that are equivalent to those days.

10

300

70

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.75

A Table for the ready finding the Decimal Parts of a year equal to any Number of Days, or Quarters of a Year. Days | Dec. Pts. | Days Dec. Pts. Days Dec. Pts. 1 1.00274

.027397 100

.273973 2 .005479 20 .054794 200 .547945 3 .008219 30 .082192

.821918 4 010959 40 .109589 360 .000000 5 .013699 50 .136986 6 016438 60 .164383 7 .019 178

.191781 of a Year .25 8 .021918 80 .219178 of a Year .50 9 .024651 90

.246575 1 )

3 of a Year Note. When the true Number of Days cannot be found at one view in this Table, then both them and their Decimals must be taken out of the Table at twice or thrice, as their Number requires, and added together. So the Decimal Parts of a year=236 days are ihus found,

2005.547945
305.082192
63.016438

EXAMPLES. 5 What will 72001 amount to in 6 years, at 5 per cent. per annum?

Ans. 95401. 6 What will 1110l 18s amount to in 12 years at 5 per cent. per annum?

Ans. 18191 is 11d 2.8qrs. 7 What will 2801 108 amount to in 3 years and 148 days, at 5 per cent. per ann. ? Ans. 3281 58 2d 3.58+qrs. 8 What will 1961 amount to in 189 days, at 4 per cent. ann. ?

Ans. 2001 1s 2d 1.23+qrs.

CASE 2. Q. When A, T. & R. are given to find P, how is it discovered?

a A. Thus:-=P trti

EXAMPLES. 1 I demand what principal will amount to 8731 19s in 9 years, at 6 per

cent.
per ann.?

Ans. 5671 10s. 2 1 demand what principal will amount to 5341 28. 8d 1.6 qr. in one year, at 5 per cent. per ann.? Ans. 5081 148.

3 I demand what principal will amount to 95401 in 63 years, at 5 per cent. per ann. ?

Ans. 72001. 4 1 demand what principal will amount to 18191 18 11d 2.8 qrs. in 12 years, at 5 per cent. per ann.? Ans. 1110) 18s.

per

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

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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

тр.

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. 8qrs. at 5 per cent?

Ans. 121 years. 5. In what time will 600l. 14s. amoant to 8711. Os. 3d. 2. 4qrs. at 4 per cent ?

6. In what time will 40001. amount to 47001. at 34 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 wbat time will 1961. amount to 2001. Is. 2ld 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.

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

-Xr: tutt=d.

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 omitteil 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 501 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. 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, rer duce the years into quarters, and work as before.

5. If 701 annuity, payable every half year, were unpaid 5 years, what will it amoưnt to in that time at 5 per cent? Aps. 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 centy Ans. 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

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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.

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