£200 at 4 months, and £400 at 6 months; but they agreeing to make but one payment of the whole, at the rate of 5 per cent. rebate, the true equated time is demanded?

Ans. 4 months, 28 days.

3. E owes F £1200, which is to be paid as follows: £00 down, £500 at the end of 10 months, and the rest at the end of 20 months; but they agreeing to have one payment of the whole, rebate at 3 per cent, the true equated time is demanded? Ans. 1 year, 11 days.

THE

COMPOUND INTEREST.

HE letters made use of in Compound Interest are,

A the Amount.

P the Principal.

T the Time.

R the Amount of £1. for 1 year at any given rate,

which is thus found:

As 100 105 :: 1: 105. Aɛ 100

Tuble of the Amount of £1 for One Year

105,5:: 1: 1,055

Table I. shews the Amount of £1. for any number of Years under

31, at 5 and 6 per cent. per annum.

1,075

10

Note: The preceding table is thus made: As 100: 105 :: 1: 1.05 for the first year; then, As 100: 105 :: 1.05: 1,1025, second year, &c. I. When P, T, R, are given, to find A.

RULE. PXA.

EXAMPLES.

1. What will £225 amount to in 3 years time, at 5 per cent. per annum? Ans. 1,05 × 1,05 × 1,05=1,157625, then 1,157625 × 225=£260...9...3. 3 grs:

2. What will £200 amount to in 4 years, at 5 per cent. per innum ? Ans. £243. .2,02bs. 3. What will £450 amount to in 5 years, at 4 per cent. per annum? Ans. £547...9...10. 2,0536368 grs. 4. What will £500 amount to in 4 years, at 5 per cent. per annum ? Ans. £619...8...2. 3,8323 grai

II. When A, R, T, are given, to find P.

a

Rule.-P. gut

EXAMPLES.

5. What principal being put to interest will amount to £260...9...3. 3 qrs. in 3 years, at 5 per cent. per annum ?

1,05 × 1,05 × 1,05=1,157625

260,465625

1,157625

£225.

6. What principal being put to interest will amount to £243 2,025s. in 4 years, at 5 per cent. per annum?

Ans. £200.

7. What principal will amount to £547...9...10. (2,0538368 grs in 5 years, at 4 per cent. per annum? Ans. £450. 8. What principal will amount to £619...8...2, 3,8323 qrs. in 4 years, at 5 per cent. ?

III. When P, A, T, are given to find R.

a

Ans. £500.

which being extracted by the rules of extraction Rule., (the time given in the question shewing the power,) will give R.

EXAMPLES.

3. At what rate per cent. will £225 amount to £260...9...3. 3 qrs. in 3 years? Ans. 5 per cent.

260,465625

225

=1,157625, the cube root of which

(it being the 3d power) =1,05=5 per cent. 10. At what rate per cent. will £200 amount to £243. 2,025.s in 4 years? Ans. 5 per cent.

11. At what rate per cent. will £450 amount to £547...9...10 2,0538368 grs. in 5 years ?

Ans. 4 per cent

12. At what rate per cent. will £500 amount to £619...8...2. 3,8323 qrs. in 4 years? Ans. 51 per cent.

IV. When P, A, R, are given, to find T,

α which being continually divided by R till othing RULE. -rt remains, the number of those divisions will be equal

to T.

EXAMPLES.

13. In what time will £225 amount to £260...9.....3. 3 grs. at 5 per cent.?

=1, the number of divisions being three times sought. 14. In what time will £200 amount to £243. 2,025s. at 5 per cent.? Ans. 4 years.

1,05

15. In what time will £450 amount to £547...9...10. 2,053068 qrs. at 4 per cent. ? Ans. 5 years.

16. In what time will £500 amount to £619...8...24,8323 at 5 per cent.? Ans. 4 years. ANNUITIES, OR PENSIONS, IN ARREARS. NOTE. U represents the annuity, pension, or yearly rent; A, R, T, as before.

Table II. shews the Amount of £1. Anuity for any number of Years under 31, at 5 and 6 per cent. per annum.

Note. The above Table is made thus: take the first year's amount, which is £1. multiply it by 1,05+1=2,05=second year's amount, which also multiply by 1,05+1=3,1525—third year's

amount.

Table continued to 100 years, see page 183

RULE.A, or by the table thus:

Multiply the amount of £1 for the number of years, and at the rate per cent. given in the question, by the annuity, pension, &c. and it will give the answer.

EXAMPLES.

17. What will an annuity of £50 per annum, payable yearly, amount to in 4 years, at 5 per cent.

Ans. 1,05 × 1,05 × 1,05 × 1,05 × 50=60,77531250 60,7753125-5

then

1,05-1

-=£215...10...1. 2 qrs. or,

by the table thus, 4,31012× 50-£215...10...1. 1,76 qrs.

18. What will a pension of £45 per unnum, payable yearly amount to in 5 years, at 5 per cent.?

Ans. £248...13...0. 3,27 gro. 19. If a salary of £40 per annum, to be paid yearly, be forborne 6 years, at 6 per cent. what is the amount?

Ans. £279...0...3 2641 20. If an annuity of £75 per annum, payable yearly, be omitted to be paid for 10 years, at 6 per cent. what is the amount? Ans. £988...11...24. 235851424346112.

II. When A, R, T, are given, to find U.

ara RULE.=U.

1.

EXAMPLES.

21. What annuity, being forborne 4 years, will amount to £215...10...1. 2 qrs. at 5 per cent.?

22. What pension, being forborne 5 years, will amount to £248...13...0. 3,27 grs. at 5 per cent.?

Ans. £45.

23. What salary being omitted to be paid 6 years, will amount to £279...0...3. 2641 at 6 per cent. ?

390626'

Ans. £40.

24. If the payment of an annuity being forborne 10 years, amount to £988.....11...24. 23585142 546112. at 6 per cent. what is the annuity? Ans. £75.

III. When U, A, R, are given, to find T.

BULE.

artu-a

which being continually divided by R, till nothing remains, the number of those divisions will be equal to T

EXAMPLES..

25. In what time will £50 per annum amount to £215...10...] 2 grs. at 5 per cent. for non-payment?

Ans.

215,50625 × 1,05+50—215,50625

50

-=1,21550625

which being continually divided by R, the number of the divisions will

be 4 years.

26. In what time will £45 per annum amount to £248...13...0. 3,27 grs- allowing 5 per cent, forbearance of payment ?

22641

Ans. 5 years. 27. In what time will £40 per annum amount to £279...0...3. Ans. 6 years. Ja, at 6 per cent. ? 28. In what time will £75 per annum amount to £988...11...2. 235851124346112, allowing 6 per cent. for forbearance of payment? Ans. 10 years, PRESENT WORTH OF ANNUITIES, PENSIONS, &c. Table III. shews the present worth of £1. Annuity for any Num ber of Years under 31, Rebate at 5 and 6 per cent.

Years.

5 Rates. 6

5 Rates. 6

Years.

14

9,29498

29

15, 14107

13,59072

15,37245

13.76483

9,89864 15 10,37965 9,71225 30 NOTE. The above table is thus made: divide £1. by 1,05= ,95238, the present worth of the first year, which÷1,05= ,90703, added to the first year's present worth 1,85941, the second year's present worth; then 90703 -1,05 and the quotient added to 1,85941=2,72324, third year's present worth, 1. When U, T, R, are given, to find P.

or, by the table, thus:

Table continued to 100 years, see page 185