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When the Interest is for any number of Days. KULE. As 365 days are to the interest of the given sum for a year, so are the days given to the interest required.

23. At 57 per cent. per annum, what is the interest of. £985 2.7 for 5 years, 127 days ?

· Ans. £989 . 15. 2. 24. What is the interest of £2726. 1. 4 at 45 per cent. per annum, for 3 years, 154 days?

Ans. £419. 15. 67 When the amount, Time, and Rate per cent. are given, to find the

Principal RULE: As the amount of £100 at the rate and time given : is to £100::so is the amount given : to the principal required

25, What principal being put to interest will amount to £402 10.0 in 5 years, at 2 per cent per annum ? 3x5+100=£115: 100:: 402... 10 20

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23\00)8050|00) £850 Ans. 26. What principal being put to interest for 9 years, will amount to £734.8.0 at 4 per cent. per annum? Ans. £540.

27. What principal being put to interest for 7 years, at 5 por cent. per annum, will amount to £334. 16.0?

Ans. £248. When the Principal Rate per cent. and the amount are given to And

the time. Rule. As the interest of the principal for 1 year : is to 1 year :: so is the whole interest : to the time required.

38. In what time will £350 amount to £402 . 10.0 at 3 por cento per annum ? £ £ s.

yrs. 350 As 10...10: 11:52...10 : 5 3 25

20

yr. £

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10150
210 2110)1050(5 years.

ans. 402...lo
20
105

350... 0 10100

52...10 29. In what time will £510 amount to £731.8.0 at 4 per cent. per annum?

Ans. 9 years. 30- In what time will £ 248 amount to £334. 16.0 at 5 per sent. per annum?

Ans. 7 years. When the Principal, Amount, and Time are given, to find tu Rate

per cent.

Rule. As the principal : is to the interest for the whole time :: so is £100 to the interest of the same time. Divide that interest by the time, and the quotient will be the rate per cent.

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31. At what rate per cent. will £350. amount to £402 . 10. in 6 years time? £402...10...0 As £350 : £52 10:: £100 : £15 350... 0 52...10...O

1050

100

350)105000(300s. £15-533 per cent. 39. At what rate per cent. will £248 amount to 2334 . 16 in 7 years time?

Ans. 5 per cent. 33. At what rate per cent. will £540 amount to £734 . 8 in 9 years time?

Ans. 4 per cent.

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COMPOUND INTEREST IS that, which arises both from the principal

and interest: that is, when the interest on money becomes due and not paid, the same interest is allowed on that interest unpaid, as was on the principal before.

Rule 1. Find the first year's interest, which add to the principal, then find the interest of that sum, which add as before ; and so on for the number of years.

2. Subtract the given sùm from the last amount, and it will give the compound interest required.

EXAMPLEX.

1. What is the compound interest of £500 forborne 3 years at 5 per cent. per aunum? 500 500

525
5
25

26...5

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25100 625 1st yerr. 551...5 2d yeur. 5

5

551... 5..0 2625 27|56.. 5 27...11...3 20

20

578... 16...3 3d year.
5100

11/25 500... 0...0 prin. sub.
12

78...16...3=interest
3100

for years. 2. What is the amount of £400 forborne 3} years, at 6 per cent. per annum compound interest? Ans. £190 : 13:111.

3. What will £600 amount to in 5 years, at 5 per cent. per annum, compound interest?

Ans. £829 : 11 : 74. 4. What is the amount of ££50 10s. for 3 years and 6 months, at o per cent. per annum, compound interest? Ans. £675:6:6.

8. What is the compound interest of £764 for 4 years and 9 months. at 6 per cent. per annum ?

Ans. £243 18.8. 6. What is the compound interest of £57. 10. 6 for 5 years, 7 in:inths, 15 days, at 5 per cent. per unnum

? Ans. £18.3.87. 7. What is the compo:md interest of £259 . 10.0 for 3 years, 9 months, and 10 days, at 4į per cent. per annum ?

Ans. £46.19.101

REBATE OR DISCOUNT S the abating so much money on a debt to be received before

1 a

the same time, and at the same rate. As £100 present money would discharge a debt of £105 to be paid a year to come, rebate being made at 5 per

cent. RULE. As £100 with the interest for the time given : is to that interest : : so is the sum given to the rebate required.

Subtract the rebate froin the given sum, and the remainder will be the present worth.

EXAMPLES. 1. What is the discount and present worth of £487. 12 for 6 months, at 6 per cent. per annum? 6 m. 6

As 103: 3:: 487 ...12

20 20
3
100

2060 9752

3 103

£ s.

206'0)29256) 14...4 rebate. 487...12

206 1.1... 4

865 Ans, £473... 8...O present worth. 824

416=ts. 2. What is the present payment of £357. 10., which was agreed to be paid nine months nence, at 5 per cent. per annum ?

Ans, £314. II. 7. 3. What is the discount of £275. 10.0 for 7 months, at 5 per cent. per annum ?

Ans. £7.16. .14. 4. Bought goods to the value of £109. 10.0 to be paiii at 9 month:s, what present money will discharge the same, if I am allowed 6 per cent. per annum discount ? Ans. £104.15.81.

3. What is the present worth of £527 . 9. I payable 7 months bence, at 44 per cent ?

Ans. £514.13. 103. 6. What is the discount of £85. 10 due September the 8th, this being July the 4th, relate at 5 per-cent. per annum ?

Ans. 153. 34.

7 Sold goods for £875.5.6 to be paid 5 months henc., what is the present worth at 4 per cent? Ans. £859, 3.34.

8. What is the present worth of £500 payable in 10 months, at 5 per cent, per unnum?

Ans. £450 9. How much ready money can I receive for a note of £75. due 15 months hence, at 5 per cent. ? Ans. £70.11.95

10. What will be the present worth of £150 payable at 3 four months, i. e. one-third at 6 months, one-third at 8 months, and one-third at 12 months, at 5 per cent. discount?

Ans. £145.3.8. 11. Sold goods to the value of £575 . 10 to be paid at two 3 months, what must be discounted for present payment, at 5

Ans. £10. 11.4. 12. What is the present worth of 2500 at 4 per cent. £100 being to be paid down, and the rest at two 6 months ?

Ans. £488.7.87

por cent. ?

EQUATION OF PAYMENTS
IS
S when several surns are due at different times to find a

mean time for paying the whole debt ; to do which, this is the common

Rule. Multiply, each term by its time, and divide the sum of the products by the whole debt, the quotient is accounted the mean time.

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EXAMPLES.

1. A owes B £200 whereof £40 is to be paid at 3 months, £60 at 5 months, and £100 at 10 months; at what time may the whole debt be paid together, without prejudice to either ?

£
40 X 3= 120
60 Х 5= 300
100 X 10=1000

m.

200) 14/20

7 months, it 2. B owes C £800, whereof £200 is to be paid at 3 months, £100 at 4 months, £300 at 5 months, and £200 at 6 months ; but they agreeing to make but one payment of the whole, I demand what time that must be ? Ans. 4 months, 17 days.

3. I bought of K a quantity of goods to the value of £360 which was to have been paid as follows: £120 at 2 months, £200 at 4. months, and the rest at 5 months; but we afterwards agreed to have it paid at one mean time, the time is demanded ?

Ans. 3 months, 12 days. 4. A merchant bought goods to the value of £500 to pay £100

at the end of 3 months, £150 at the end of 6 months, and £250 at the end of 12 months; but afterwards they agreed to discharge the debt at one payment; at what time was this payment made ?

Ans. 8 months, 11 days. 5. H is indebted to L a certain sum, which is to be paid at 6 different payments, that is, į at two months, ; at 3 months, at 4 months, 4 at 5 months, at 6 months, and the rest at 7 months; but they agree that the whole shall be paid at one equated time, what is that time? Ans. 4 months, 1 quarter.

6. A is indebted to B £120 whereof is to be paid at s months, į at 6 months, and the rest at 9 months, what is the equated time of the whole payment ? Ans. 5 months, 7 days.

BARTER IS. the exchanging oue commodity for another, and informs

the traders so to proportionate their goods, that neither may sustain loss.

RULE 1st, Find the value of that commodity whose quantity is given : then find what quantity of the other, at the rate proposed you may have for the same money.

2dly. When one-has goods at a certain price, ready money, but in bartering advances it to something more, find what the other ought to rate his goods at, in proportion to that advance, und then proceed as before.

EXAMPLES 1. What quantity of choco 2. A and B barter; A hath late at 45. per lb. must be deli- 20 cwt. of prunes, at-4d. per lb. vered in barter for 2 cwt. of tea ready money, but in barter will at 94. per lb.

have 5d, per lb. and B hath hops

'orth 328. per cwt. ready money; 2 cwt.

vhat ought B to rate his hops at 119

1:2 barter, and what quantity

must be given for te 20 cwt. of 224

Hirunes ?

d. d. 9

119 As 4:5:: 32 20

5 4/2016 the value of the tea.

40 2240

4)160 An. 604 16. ehocolate,

12

5

cwt. gr. 16. 40s. 48|0)1120,00 23...1.. 9 Ans.

96

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