25. Find in what time £963,, 10s. 6d. will amount to £988,, 168.,, 4,83d. at 31 per cent. Simple Interest.

26. At what rate of Simple Interest will £225 „, 68. „, 8d. gain £3,, 138.,, 24d. in 6 months?

27. In what time will £450 amount to £516,, 188.,, 9d. at 3 per cent. Simple Interest?

28. What is the capital which, put out at 3 per cent. Simple Interest for 5 years and 4 months, will amount to £9973 68.,, 8d.?

29. When in 2 years and 63 days the Simple Interest on £325 is £24 148.,, 34d., what is the rate per cent. per annum ?

30. In what time will the Interest upon £320, 128. 6d. be £70,, 108. 9d. at 4 per cent. Simple Interest?

31. What principal, put out for 6 years at 4 per cent. Simple Interest, will amount to £1002 198.,, 71d.?

32. What is the rate of Simple Interest when £315,, 68.,, 8d. will amount to £359,, 9s.,, 7d. in 4 years?

33. In what time will £150,, 158. amount to £175, 18. „, 21 d. at 4 per cent. Simple Interest?

34. What capital would be required to gain £12,, 18.,, 0žd. in 2 years and 5 months at 34 per cent.?

99

35. What must be the capital employed to gain £95 68.,, 4d. as interest in 3 years at 42 per cent. Simple Interest?

36. If 128.,, 4d., when left in a Savings Bank for 5 years, gained 38.,, 0d., what was the rate of interest allowed?

EXERCISE XVII.

COMPOUND INTEREST.

1. Find the amount of £250 in 2 years at 33 per cent. Compound Interest.

2. What is the amount of £690 for 3 years at 4 per cent. Compound Interest?

3. Find the amount of £1000 for 4 years at 5 per cent. Compound Interest?

4. Find the amount at Compound Interest of £363, 10s. for 4 years @ 5 0/0.

5. What is the Compound Interest on £300 at 4 per cent. per annum for 2 years, if the interest be paid half-yearly?

6. Find the interest on £20000 for 4 years at 3 per cent. Compound Interest.

7. Find the Compound Interest on £750 for 2 years at 4 per cent.: also the amount of the same sum in 2 years if the interest be payable half-yearly.

8. If the sum of £1200 be put out at 10 per cent. per annum Compound Interest, and the interest be paid halfyearly, to what will it amount in a year and a half?

9. Find the difference between the Simple and Compound Interest of £2475, 13s. „, 4d. for 2 years at 3 per cent. 10. Find the amount of £540 in 3 years at 4 per cent. Compound Interest.

11. Find the amount of £130 in 3 years at 5 per cent. Compound Interest.

12. Find the amount of £769 in 4 years @ 4 0/0 Compound Interest.

13. Find the difference between the Simple and Compound Interest on £150 15s. for 3 years at 4 per cent.

14. What sum must be put out to Compound Interest for 21 years at 3 per cent. to amount to £174.39543 ?

15. What is the difference between the amount of £250 accumulating during 3 years at 3 per cent. Compound Interest, and the amount of the same sum for the same period at 4 per cent. Simple Interest?

16. Find the Compound Interest on £1563 19s.,, 8d. for 23 years at 3 per cent.

17. Find the difference between the amount at Simple and Compound Interest of £895,, 16s. for 2 years at 3 per cent.

18. At 3 per cent. Compound Interest, what capital will amount to £289,, 48.,, 7.38d. in 2 years?

19. Find the amount of £415,, 10s. in 2 years at 4 per cent. Compound Interest.

20. What is the amount of £230,, 10s. for 3 years at 3 per cent. Compound Interest.

21. What would £25,, 12s. amount to in 3 years at 4 per cent. Compound Interest ?

22. In 3 years at 4 per cent. Compound Interest what would £1080 amount to?

23. What is the Compound Interest on £3350 at 4 per cent. per annum for 2 years, if the interest be paid halfyearly?

24. What sum must be put out at 10 per cent. Compound Interest to amount in 3 years to £1597 48.?

25. Find the sum of money which in 4 years at 5 per cent. Compound Interest will amount to £881 „, 4s. „, 107d.

CHAPTER XV.

DISCOUNT.

§ 99. The principle upon which the Rule of Discount depends, being frequently misunderstood, the following explanation should be read attentively:

When a debt due at some future time,-not a Tradesman's Account, but a Bill, or a Promissory Note, or the Reut of a House, or any debt which cannot be claimed at present, but which will fall due some time hence-when such a debt is paid before it is due, a sum smaller than the actual debt may be paid down by the Debtor, and will be accepted by the Creditor as payment in full.

The reason why the Creditor accepts a sum smaller than his full due is because he would at once put out to interest the money he receives from the Debtor; thus, whatever he will gain as interest he can afford to remit from the debt; and this principle will be manifestly fair to both payer and receiver.

Now call the sum accepted as the present payment, the Present Worth: and call the money that is thrown off, the Discount. The Present Worth must be such a sum as would, if put out to interest for the given time at some agreed on rate, amount to the debt; and the interest it would gain in

that time must be the sum remitted, or the Discount. Hence we deduce the following:

Def. The Present Worth of any debt due at some future time is the smaller sum accepted at the present time in lieu of the entire debt at the future time; and is such that, if put out to interest at a given rate for the time during which the debt had to run, it would at the end of that time amount to the debt itself.

Def. Discount is the abatement made in consideration of the payment of a debt before it is due; and is the simple interest of the present worth of the debt.

and

Hence

debt-discount=present worth,

debt-present worth discount.

From these definitions we can shew that the discount of a debt must always be less than the interest upon it for the same time. For (1) the discount is the interest upon the present worth; but the present worth is always less than the debt; and therefore the interest on the present worth will always be less than the interest on the debt; or the discount on any sum will always be less than the interest of the same sum for the same time.

Again, (2) since present worth+discount = debt, it follows that if the debt in a certain time would give certain interest, we may say that in the same time present worth + discount, if put out to interest, would amount to debt + interest. But by the definition, the present worth would amount to the debt; therefore the discount would amount to the interest; that is, the discount is the present worth of the interest.

§ 100. We see from both these considerations that interest is really greater than discount: yet the two are commonly confused, discount being frequently supposed to be the same thing as interest. This is perhaps to be accounted for by these two circumstances; first, tradesmen as a rule deduct interest from an account, and call it discount; an element of confusion which will be more fully explained below, in § 103; secondly, the terms in which the questions are expressed sometimes lead to a mistaken notion; for instance, if it be required to find the present worth of any sum "allowing discount at 5 per cent.," it is taken for granted that this means "throwing off £5 from every £100;" whereas in reality the

first thing in allowing discount is for the payer and receiver to agree upon the rate at which the interest on the present worth is to be calculated; and then "allowing discount at 5 per cent." will not mean throwing off £5 from every £100; but will mean "allowing discount when the rate of interest agreed on is 5 per cent."

§ 101. We now proceed to explain the practical rule for finding the discount of any sum.

If £100 were due a year hence, and if £95 were accepted as the present worth of this debt, the £95 being put out to interest at 5 per cent. would not gain £5, and would not amount to £100 at the end of the year: and £5 would be too large a sum to allow as the discount on £100 for a year.

But if £105 were due a year hence, and £100 were accepted as the present worth, the £100 being put out to interest at 5 per cent. would gain £5, and would amount to £105 at the end of the year.

Hence, we observe that £5, the interest on £100 for a year, is the discount on £105 for the same period: and generally, the same sum that is the interest of £100 for any time, will, for the same time, be the discount of £100 increased by that interest.

The rule therefore for finding the discount on any sum will be this: 66 First find the interest upon £100 for the given time at the given rate, and add it to the £100: the sum found as interest on £100 will be the discount on the £100 increased by its interest: then the discount on any other sum for the same time at the same rate can be found by proportion."

This will now be illustrated by examples:

Ex. 1. Find the Discount on £770 due 8 months hence, allowing interest at 4 per cent. per annum.

therefore interest at 4 per cent. on £100 for 8 months

therefore £23 is discount on £1023 for 8 months.