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RULE FOR PROBLEM IV.

Divide the given interest by the Int. of $1 for the given time at the given rate per cent.; the quotient will be the principal. Or, by PROPORTION. As the Int. of $1 for the given time, at the given rate per cent., is to the given Int., so is $1 to the required principal.

What Principal,

3. At 5 %, will gain $341.25 in 3 yr.?

Ans. $2275.

4. At 6 %, will gain $2.26 in 16 mon.? Ans. $28.25
5. At 5 %, will produce a yearly interest of $1023.75?
Ans. $20475.

6. At 9 %, will gain $525.398 in 12 yr. 3 mon. 20 da.? Ans. $174.40 PROBLEM V. To find the PRINCIPAL and INTEREST, the Time, Rate per cent., and Amount being given.

This is treated of under Discount.

See Art. 238.

ART. 233. COMPOUND INTEREST

Is interest on the principal, and also on the interest itself, after the latter becomes due.

(Simple Interest is interest on the principal only.)

1. Find the compound Int. of $300 for 3 yr. at 6 %.
$300. Principal 1st year.

$300X.06= 18. Interest

1st year.

10. At 4 10

11. At 5 %? A

$318. Principal 2d year.
19.08 Interest 2d year.

337.08

Principal 3d year.

12. At 7 %? Ans..

13. At 8%? Ans. 20.2248 Interest 3d year.

17. In what time, a itself? Ans. 13 yr.

ART. 231. PROBLEM CENT., the Principal, I

3048 Amount for 3 yr.
Given principal.

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REVIEW.-230. How find the itself, at any given rate per cent. ?

18 Compound Int. for 3 yr.

terest of $200 for 2 years, Ans. $33.28

231. What is problem III? What the What the Rule for Prob. IV?

RULE FOR COMPOUND INTEREST.

Find the amount of the given principal (Art. 222) for the 1st yr., and make it the principal for the 2d yr.

Find the amount of this principal for the 2d yr., make it the principal for the 3d yr., and so on, for the given number of yr. From the last amount subtract the given principal; the remainder will be the compound interest.

NOTES.-1. When the interest is payable half-yearly, or quarteryearly, find the Int. for a half, or a quarter year, and proceed in other respects as when the Int. is payable yearly.

2. When the time is years, months, and days, find the amount for the years, then compute the Int. on this for the months and days, and add it to the last amount.

Find the Amount, at 6 %, Compound Interest,

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8. Find the amount of $500 for 2 yrs., at 20% compound interest, payable quarterly. Ans. $738.727+ 9. What is the compound interest of $300 for 2 yr. 6 mon., at 6%? Ans. $47.192+ 10. What the compound interest of $1000 for 2 yr. 8 mon. 15 da., at 6% ? Ans. $171.353

ART. 234. Since the amount of $2, for any given time, will be twice the amount of $1; the amount of $3, three times as much, &c.; Therefore,

If a table be formed containing the amounts of $1 for 1, 2, 3, &c., years, any of these amounts multiplied by a given Principal will give its amount at Compound Interest for the sam tine and rate. See Table, page 238.

TABLE

Showing the amount of $1, at 3, 4, 5, 6, 7 and 8 per cent., Compound Interest, for any number of years, from 1 to 25.

Yr. 3 per cent. 4 per cent. 5 per cent. G per cent.

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7 per cent. 8 per cent.

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1.125509 1.169859 1.215506
1.159274 1.216653 1.276282
1.194052 1.265319 1.340096
1.229874 1.315932 1.407100
1.266770 1.368569 1.477455
1.304773 1.423312 1.551328
1.343916 1.480244 1.628895

1.503630.
1.593848 1.718186 1.850930
1.689479 1.838459 1.999004
1.790848. 1.967151 2.158924

10

11

12

1.384234 1.539454 1.710339
1.425761 1.601032 1.795856

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11. What, by the Table, will be the Amount of $70 for

9 yr., at 5 % compound interest?

SOLUTION. By the Table, the amount of $1 for 9 yrs., at 5 pr. ct., is $1.551328; and $1.551328X70=$108.59296

12. Of $345 for 10 yr., at 6 %?

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Ans. $617.84+

EXPLANATION.—Take any two periods whose sum is 41 years, thus, 20 yr.+21 yr. 41 yr., and find the amount for the 1st period: then regard this a new principal, and find its amount for the 24 period: the last amount will be the Ans.

The Tabular number for 20 yr. is 3.207135; this, multiplied by 200, gives $641.427, amount for 20 yr.: Tabular number for 21 yr. is 3.399564, which×641.427—$2180.572+ Ans.

What, by the Table, will be the Interest 14. Of $890 for 30 yr., at 6% ?

15.

Ans. $4221.70+

$200 for 70 yr., at 5% ?

Ans. $5885.28+

ART. 235. DISCOUNT

Is a deduction made for the payment of money before it is due. For example,

If a debt of $106, duc one year hence without interest, be paid at the present time, the sum paid, with one year's interest added, should make $106. And,

If the rate per cent. is 6, this sum would be $100; for, the amount of $100 at interest for 1 year, at 6%, is $106. Art. 220.

The PRESENT WORTH of a debt payable at a future time without interest, is that sum which, at a specified rate % for the same time, would amount to the debt.

The DISCOUNT is the sum deducted for present payment.

ART. 236. 1. Find the Present Worth of $224, due 2 y yr. hence, without interest, money being worth 6% per annum.

SOLUTION. The amount of $1 for 2 years, at 6 per cent., is $1.12; hence, the present worth of each $1.12 of the given sum, is $1. And, the present worth of $224, will be as many times $1, as $1.12 is contained times in $224.

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PROOF. The amount of $200 for 2 years, at 6 per cent., is $224. Art. 220.

2. Find the present worth of $81, due 2 yr. hence, no Int., money worth 4 % per annum.

Ans. $75.

REVIEW. 234. What does the Tabie show? By means of it, how find the amount of any sum at compound interest?

235. What is discount? What the present worth of a debt, payable at a future time without interest? The discount?

OF PRESENT WORTH.

To find the present worth of a sum payable at a future time without interest:

Rule.-Divide the given DEBT by the amount of one dollar for the given time, at the given rate per cent.; the quotient will be the PRESENT WORTH.

To find the DISCOUNT, subtract the PRESENT WORTH from the DEBT.

Or, by PROPORTION. As the amount of any principal, (as $1, or $100,) for the given time, at the given rate per cent., is to the principal, so is the given debt to the present worth.

NOTE. In the following Examples, the rate per cent. is 6, unless some other is given; and when the present worth of any sum is required, it is supposed not to be at interest.

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$29.64

$55.00

11. $276.64 due 2 years hence?. 12. $330.00 due 3 yr. 4 mon. hence? 13. Bought $260 worth of goods, on what sum will pay the debt now?

14. If money is worth 12 %, what worth of $235.20, due 1 year hence?

15. What is the discount, at 7 %, of year hence?

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8 mon. credit: Ans. $250. is the present Ans. $210. $101.25, due 1 Ans. $26.25

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