COMPOUND INTEREST.

249. COMPOUND INTEREST is interest on both principal and interest, the latter not being paid when it becomes due. The principal may be increased by adding the interest to it annually, semi-annually, quarterly, etc., according to agreement, and the creditor may receive compound interest without being liable to the charge of usury (Art. 231), though he cannot legally collect it if the debtor refuses to pay.

250. To calculate Compound Interest:

RULE. Make the AMOUNT for the FIRST year or specified time, the PRINCIPAL for the SECOND; the amount for the SECOND the principal for the THIRD; and so on. From the LAST AMOUNT subtract the FIRST PRINCIPAL, and the REMAINDER is the compound interest.

Ex. 1. What is the compound interest on $100 for 3yr. 3m., at 6 per cent. per annum?

20.88 8 12 4 Com. Int. for 3yr. 3m.

NOTE 1. Find the amount for the years as though there were no months in the given time, and this amount is the principal for the remaining months.

249. Compound Interest, what is it? How often may the interest be com pounded? May the creditor receive compound interest if the debtor chooses to pay? Can he collect it if the debtor refuses to pay? 250. Rule for computing compound interest? Rule when there are months and days in the given time?

2. What is the compound interest on $200 for 2yr. 8m., at 4 per cent. per annum. Ans. $22.089.

3. What is the compound interest on $500 for 3 years, at 7 per cent.? Ans. $112.5215.

4. What is the amount of $5000 at compound interest, for 4yr. 10m. 12d.? Ans. $6640.629. 5. What is the amount of $3000 at compound interest for 2yr. 6m. 18d ? Ans. $3482.036. 6. What is the compound interest of $10000 for 2yr. 6m. 18d., at 6 per cent.? Ans. $1606.788. 7. What is the compound interest of $10000 for 2yr. 6m. 18d., at 4 per cent.? Ans. $1053.952. 8. What is the compound interest of $10000 for 2yr. 6m. 18d., at 8 per cent.? Ans. $2177.216.

NOTE 2. Four per cent of any number is, and 8 per cent is of 6 per cent of the same number, but the compound interest of any sum of money at 4 per cent. is less than of the compound interest of the same sum for the same time at 6 per cent., and the interest at 8 per cent. is more than of the interest at 6 per cent., as may be seen by examples 6, 7, and 8.

The compound interest at 4 per cent. is less than half the compound interest of the same sum at 8 per cent, because the base of percentage, (i. e. the principal,) after the 1st year, is less in computing interest at 4 per cent. than in computing it at 8 per cent.; thus, in computing interest at 4 and 8 per cent. the 1st year the base is the same, and one interest is just half of the other; but the 2d year one base is $104 and the other $108; .. the interest at 4 per cent. is less than half of that at 8 per cent.

9. What is the amount of $250 for 2yr. 6m., at 3 per cent. for each 6m., compounding the interest semi-annually?

Ans. $289.818.

10. What is the interest of $36 for 1yr. 9m., at 2 per quarter, compounding the interest quarterly?

per cent.

Ans. $5.352.

11. What is the compound interest of $864.75 for 3yr. 8m. 15d., at 6 per cent.? Ans. $208.953. 12. What is the compound interest of $327.54 for 4yr. 4m. 8d.?

250. Is compound interest at 4 per cent. half as much as at 8 per cent.? Why?

251. Compound interest may be calculated more expeditiously by means of the following

TABLE,

Showing the Amount of $1, £1, etc., interest compounded annually at 4, 5, 6, 7, and 8 per cent., from 1 to 20 years.

6

7

8

10

11

12

1.338226- 1.402552- 1.469328+

7

8

9

1.265319+ 1.340096- 1.418519 1.500730+ 1.586874+ 1.315932- 1.407100+ 1.503630+ 1.605781+ 1.713824+ 1.368569 1.477455+ 1.593848+ 1.718186+1.850930+ 1.423312- 1.551328+ 1.689479- 1.8384591.9990051.480244 1.628895- 1.790848 1.967151+ 2.158925- 10 1.539454+ 1.710339+ 1.898299-2.104852-2.331639- 11 1.601032+ 1.795856+ 2.012196+ 2.252192-2.518170+ 12 1.665074- 1.885649 2.132928+ 2.409845+ 2.719624- 13 14 1.731676 1.979932- 2.260904- 2.578534-2.937194- 14 1.800944 2.078928+ 2.396558+ 2.759032- 3.172169+ 15 1.872981 2.182875- 2.540352- 2.952164 3.425943- 16 1.947900+ 2.292018+ 2.692773- 3.158815+ 3.700018+ 17 2.025817- 2.406619 2.854339+ 3.379932+3.996019+ 18 2.106849 2.526950+ 3.025600- 3.616528- 4.315701 19 20 2.191123+ 2.653298 3.207135+ 3.869684+ 4.660957+ 20

13

15

16

17

18

19

NOTE. The interest is $1, £1, etc., less than the amount in the above table. 13. What is the compound interest on $600 for 20yr.? $2.20 7135 =Int. of $1 for 20yr. taken from the Table.

600

$1 3 2 4.2 8 1000 Int. of $600 for 20yr., Ans.

14. What is the compound interest on $30 for 5yr. 6m.?

$11.35 11 8 3 4 0 = Int. of $30 for 5yr. 6m., Ans.

15. What is the amount of $50, at 7 per cent. per annum, for 15yr. at compound interest?

$ 2.7 5 9 0 3 2 = Amount of $1 for 15yr.

50

$137.951600= Amount of $50 for 15yr., Ans.

16. What is the amount of $350.50, at 8 per cent. compound interest, for 18 years?

17. What is the compound interest of $75 for 20 years, at 8 per cent.?

18. What is the interest of $500 for 9yr. 6m., at 4 per cent. for each 6 months, compounding the interest semi-annually?

Ans. $553.425.

19. What is the amount of $100 at compound interest for 40 years, at 7 per cent. per annum? Ans. $1497.445. 20. What is the amount of $100 at compound interest for 30 years, at 6 per cent. per annum?

DISCOUNT.

252. DISCOUNT is an abatement or deduction made for the payment of a debt before it is due.

The PRESENT WORTH of a debt, payable at a future time without interest, is, evidently, a sum which, put at legal interest, will amount to the debt at the time of its becoming due.

The debt, then, is an amount, the present worth is the principal, and the discount is the interest of this principal. Hence,

253. The rule for finding the present worth is that given in Prob. 4, Art. 248, viz.:

Divide the given sum by the AMOUNT of $1 for the given rate and time.

The DISCOUNT is found by subtracting the present worth from the face of the debt.

252. What is Discount? Present Worth? The debt is the same as what in Art. 248? Present Worth? Discount? 253. Rule for finding present worth?

Discount? Explain Ex. 1.

Ex. 1. What is the present worth of $37.44, due in 8 months? What the discount?

2. What is the present worth of a debt of $100, payable in one year, without interest? What the discount?

Ans. Present worth, $94.339+; discount, $5.6613. What is the present worth of $1319.29, due in 2yr. 11m.? Ans. $1122.80. 4. What is the present worth of $141.50, due in lyr. 3m. 15d.? Ans. $131.32+. 5. What is the present worth of $346.87, due in 2yr. 4m. 12d.? Ans. $303.74-. 6. What is the discount on $456.25, due in 9m. 12d.?

Ans. $20.48.

7. What is the present worth of $490.50, due in 1yr. 6m.? What the discount?

8. What is the discount on $315, due in 1 year, at 5 cent.?

per

9. I have a note for $1000, payable May 1, 1863; what discount shall I make for payment to-day, Aug. 19, 1862, money bearing interest at 10 per cent. per annum? Ans. $65.42.

NOTE. The interest on the present worth equals the discount on the

debt.

10. What is the interest for 6 months on the present worth of a note for $350, due 6 months hence? Ans. $10.19. 11. What is the interest for a year on the present worth of a note for $756, due 1 year hence?

12. I have a note for $436, payable June 21, 1863; what is the worth of the note to-day, May 12, 1863, money being worth 8 per cent. per annum?

13. What is the discount on $896, due in 1yr. 8m.?

14. What is the present worth of $475, due in 2yr. 4m. 12d.?