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ARITHMETIC.--LESSON 3.-COMPOUND INTEREST.

Note. Compound Interest is that which accrues on the amoant of the principal and interest. That is, the interest for the given time is added to the principal, and the amount constitutes a principal for another given time, and so on. The time may be three, six, or twelve months, as the parties may agree.

RULE 1. Find the amount of the given principal, at the given rate and time, as in simple interest, which will form a new principal for another period of time.

2. Subtract the first principal from the last amount, and the remainder will be the Int. Thus:

(1) What is the compound interest of $150 for 5 years, at 4 per cent. a year? 150 X.04=6.00 Int. for 1 year, and 150+6.09=$156, am or principal for 2d year. 156 X.04=6.24 Int. 2d year, and 156+6.24=$162.24 amt or principal for 3d year. 162.24X.04=6.489 Int. 3d year, and 162.24+6.489=$1687 729 amt. or principal for 4th year. 168.729 X.04=6.749 Int. 4th year, and 168.729+-6.749 $175.478 amt. prin. 5th year. 175.478 X.04=7.019 Int. 5th year, and 175.47847.0195 $182.497 amt. 5th year.

Then.
$182.497-150=$32.497 com. int. for 5

years.

Ans. (2) What is the compound Int. of $210.50 for 3 years, at 6 per centa year?

Ans. $29.49 Obs. When months or days make a part of the time, find the simple interest for such time, and add it the compound interest.

(3) What is the compound Int. of $100 for 7 10-12 years, at 6 per cent. a year?

Ans. $57.823 (4) What is the compound Int. of $760 for 3 years, at 6 per cent. a year.

Ans. 154.17 (5) What is the amt. of $1300 for 3 years, at 5 per cent. a year, compound Int.

Ans. $1504.91 (6) What is the compound Int. of $2162.50 for 3 1-2 years, at 7

Ans; 573.31 per cent. a year?

D2

Prin. first year $2162.5

.07 Rate per cent

151.375 Int. first

year. 2162.5

Prin. second year, 2313.875

.07 Rate per cent.

161.97125 Int. 2d year. 2313.875

Prin. third year, 2475.84625

.07 Rate per cent.

1-2 year, 173.3092375 Int. 3d year.

86.65466875 Int. 1-2 years. 2475.8462

2735.81015625 Amount.
2162.5

First prin.

$573.31015625 Ans. Note. This is done by decimals, and it is the safest and most expedia. itious mode of computing compound interest in federal money.

FALSE SYNTAX.LESSON 4.

Rule 2. Relative pronouns must agree with the nouns for which they stand, in person, number, and gender. As, the boy who reads with you, speaks well, &c.

Note. Every relative pronoun, must have a noun to which it refers, either expressed or implied. And as the relative stands for the noun, it of course, partakes of all its properties:-hence, the verb agrees with it, as it would with the noun, if used. Now, as the relative pronoun has in itself no distinction of number, it follows that reference must be had to the noun to determine its agreement, &c.

The man which seeks wisdom shall find her.

This sentence is faulty, because the relative which, refers to the noun, man, whereas it can belong oniy to the brute creation and inanimale objects; hence, which, should be who. Thus:The man who seeks, fc.

The exercise of reason appears as little in these sportsmen, as in the brutes whom they hunt, and by who they are hunted. The wheel killed another man, which is the sixth which have lost their lives by this means.

Obs. The relative that, is applied to persons and things after the superlative degree of the adjective, and the adjective pronoun, some.

Thus:-Washington was the greatest man that the world ever saw,

He is the same man that led our armies in the memorable Revolution.

Moses was the meekest man who we read of. Humility is one of the most amiable virtues which we possess.

Obs. 2. In writing and speaking, a proper and deterninate. use, and a clear perspicuous reference to the relative, should be carefully preserved.

The disciples of Christ whom we imitate. This is obscure language, for it does not appear which is imitated, Christ or his disciples.

The king dismissed his minister without enquiry, who had never before done so unjust an act.

OBS. 3. Whom, which, what, and that, though put in the objective case, are placed before the verb. As, whom seek ye? What seek ye? What, often represents two cases. As; he likes what I dislike, fic. He heard what the party said, f.c.

SPELLING.- LESSON 5. Rib-er-tine lib/ber-tin mys-te-ry mis'tē-re lic-or-ice lik'kůr-is mys-ti-cal mis'te-kăl lig-ne-ous lig 'nė-ūs

pick-er-el pik kūr-il lin-e-age lin'ne-aje pil-fer-er

pil'fŭr-ŭr lin-e-al lin'nē-ăl pil-grim-age pilgrim-aje lin-e-ar lin'nē-år pil-lor-y

pil'lūr-ē li-qua-ble lik'we-b1 pin-na-cle pin'nă-kl li-qui-date lik'we-date pit-e-ous pitsh'ê-ús lit-an-y lít tăn-prim-i-tive prim'ē-try lit-er-al lit-tér-əl pris-on-er

priz'zon-úr - ht-i-gate

priv-i-lege priv'vē-lidje: lit-ur-gy

priv-i-ly priv'ē-lē liv-er-y liv'věr-e

piră-mid mich-ael-mas. mikskěl-mūs quir-is-ter kwer'ris-tūr mil-ia-ry mily3 - rẽ rib-ald-ry rib'băld-re mil-lin-er millin-nŭr rick-et-y rik'it-ê mim-ic-ry mim'mik-rē rid-i-cule rid'ê-kūle min-is-ter min'nis-túr rig-or-ous rig'gúr-us

lit'te-gate lit'tür.jē

pyr-a-mid

min-strel-sy min'strėl-sē ris-i-ble riz'e-b7 min-u-et min'nū-it rit-u-al rit'yū-al mir-a-cle mir'ă-kl riv-u-let riy’ū-lēt mis-an-thrope mis'ăn-thrõpe scin-til-late sin'til-late mis-chiev-ous mis'tshěv-ús script-u-ral skript'yū-rål mis-a-ble mis'se-bl sig-ni-fy sig'nē-fi mis-cre-ant mis krē-ănt sim-i-lar sim'ē-lur mis-er-y miz'zūr-ē sim-i-le sim'ē-le mis-tle-toe miz'zl-to sim-ple-ton sĩm'pl-tún mit-i-gate mit'te-gate sim-ple-fy sim'ple-fi mit-ti-mus mit'te-mus sing-u-lar

sing'gū-lăr myr-i-ad mir'rē-ad sin-is-ter sin'nis-túr

LESSON 6. Application of the Inflections, 8.c. Virtue is the foundation of esteem', and the true source of happiness'; for beauty will fade', wit will depart', learning will vanish', and the arts will decay':--but virtue survives the ruins of time! Bind to your bosom', by the most endearing ties of affection', your brothers' and your sisters'; cherish them as your best companions through the variegated journey of life', and let no jealousies' or contentions' disturb the harmony of

your home'.

That portion of your life which is passed, is gone for every and that which is to come may be very short ;-- hence the present is all you have :with what solicitude should you ent ploy it!

This is the state of man',--to-day he puts forth the tender leaves of hope';~-to-morrow he blossoms and bears his blushing honours thick around him'; but the third day comes a frost';

-a killing frost', and nips his root man dies'. The immortal mind may leave the straw thatched cottage, with less regret', perhaps', than the splendid palace'; --and the crumbling dust may rest as quietly beneath the grassy turf'; as under the parade of a costly monument'.

Those who are accustomed to view their companions in the most favourable light', are like persons who dwell amidst those beautiful scenes of nature on which the eye rests with peculiar pleasure'; but the suspicious', are like the traveller in the wilderness';--he sees no objects but such as are dreary' or terrible'.

COMPOUND INTEREST-LESSON 7. Nate 1. When the given principal is in sterling money, it will be

found most convenient to reduce the parts of a pound to decimals. See the rule 262 page, 2d part.

(7) What is the com. Int. of $760-10 for 4 years, at 4 pr. ct. a year?

$760.5 X.04=£30.420 Int. +760,5=790.92 amt. of one year €790-92 X.04=31.6368+790.92=#822.5568 amt. 2 yr. £822.5568 X.04 = 32.902272+822.5568 = £855.4590.72 amt 3 year.

£8558.459072X.04=34,21836288+855.459072=£889.67743488 amt. 4 year. £889.67743488-760.55£129. 17743488

20

3.54869760

12

6.58317120

4 Ans.

2.03268480 or £129-3-6-2 Note 2. For the reduction of this decimal, see page 264, second part.

(8) To what will £80-4 amt. in 9 years 4 mon. at 6 pr. ct. per ann. com. Int.

ins. £128-3-0-2 Note. 3. The following mode is some times adopted, which by many is thought preferable, especially in the computation of com. Int. on Federal money. 1st find the amt. of $1 for one year at the given rate, and involve that amt, to a power equal to the given time, less

by one. 2d multiply the last product by the principal, and the result will be the amount; Thus:-

(9) What is the Int. of $210.50 for 3 years, at 6 pr. ct. & year?

$1X06=06+$1=$1.06 amt. of one dollar for one year, at 6 per cent.

1.06X1.06=1.1236 X1.06=1.191016. X 210.50=250** 705--210.50=$40.205 Ans.

Note 4. When the given time is years and parts of years, find the amt, of $1. for one year, and for the months, &c. take the even parts and then work as above.

FALSE SYNTAX.LESSON 8. RULE 12. When no subject comes between the relative med the verb, then the relative is the subject, and the verb

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