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2. Find the int. of $264.80 for 3 mo. 21 da., at 8%; also,

of $648 for 4 mo. 12 da., at 71%.

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4 mo. 12 da. as 43, or 22 mo.,

360

111 Years.

{108

or as 132 da.;

71% as 15%.

and the rate
Either form 1875

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may be used, as most con

$6.53 Int.

venient.

$17.82 Int.

3. Find the int. of $840 for 18 da., at 11% a mo.; for 3 mo. 10 da., at 2% a mo.; for 5 mo. 22 da., at % a mo.; and for

93 da., at 4% a mo.

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EXPLANATION.-It is plain that 11% a mo. is 18% a year; 2% a mo.

is 24% a year; % a mo. is 9% a year; and % a mo. is 48% a year. So many illustrative examples have been given, that the simplicity and practical utility of this method might be apparent.

By any of the preceding methods, find the interest

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23. If a man borrow $9700 in N. Y., at 6%, and loan it in Colorado, 10%, what will it gain in 1 yr. 6 mo.?

24. A person borrows $3754.45, being the property of a minor who is 15 yr. 3 mo. 20 da. old. He retains it until the owner is 21 yr. old. How much money will then be due at 6%.

25. A note for $710.50, with interest after 3 mo., at 7%, was given Jan. 1, 1884, and paid Aug. 12, 1886. What was the amount due?

26. A speculator borrowed $9675, at 6%, April 15, 1884, with which he purchased flour at $6.25. May 10, 1885, he he sold the flour at $73 a barrel, cash. What did he gain by the transaction?

27. A man, engaged in business with a capital of $21840, is making 124% per annum on his capital; but on account of ill health he quits his business, and loans his money at % a month. How much does he lose in 2 yr. 5 mo. 10 da. by the change?

28. Bought 4500 bu. of wheat at $1.12 a bushel, payable in 6 mo.; I immediately realized for it $1.06 a bushel, cash, and put the money at interest at 10%. At the end of the 6 mo. I paid for the wheat. Did I gain or lose by the transaction, and how much?

PROBLEMS IN INTEREST.

299. Since interest is the product of the three factors, principal, rate, and time (293), any one of these three factors may be found by dividing the interest by the product of the other two. Hence,

The general formula, I= Px Rx T, produces the following formulas. Observe that I, divided by the product of any two letters of the three, P, T, R, equals the other one.

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The above is a brief substitute for the numerous rules given in the books, and is simple and easy to be remembered. The pupil may be required to construct a rule for each.

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300. Find each one of the four elements in the following example, from the other three, by the above formulas.

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If the amount is given instead of the interest, divide it by the amount of $1 at the given rate and time; thus,

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The preceding brief formulas will enable the pupil readily to solve all problems pertaining to interest.

In using the vertical line and cancellation, it will be remembered, that numerators or dividends are placed on the right, and denominators or divisors on the left, and that to divide by a fraction we invert the terms. The time should be expressed in years; thus, 2 yr. 6 mo. is 2 or 2.5 yr.; 1 yr. 4 mo. is 13 or 3 yr.; 9 mo. is, or, or .75 yr.; 7 mo. is yr.; 2 mo. 12 da. is 7 yr., etc. The result will be in years and deci mals of a year, which may be reduced to months and days (198).

72

In the following examples, find each one of the elements:

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4. Will gain $173.97 in 4 yr. 4 mo. at 6%? At 12%?
5. Will gain $153.75 in 3 mo. 24 da. at 7%? At 8%?
6. Will amount to $1596 in 2 yr. 6 mo. at 51%?

7. Will amount to $1531.50 in 3 mo. 18 da. at 7%? At what rate %

8. Will $350 gain $70 in 2 yr. 6 mo.?

9. Will $550 gain $220 in 5 yr. 4 mo. ?

10. Will $2085 gain $68.11 in 5 mo. 18 da. ?

In what time will

11. $245 gain $2.94 at 6% ? 13. $550 amt. to $576.95 at 7% ? 12. $600 gain $132 at 8%? 14. $204 amt. to $217.09 at 51%? 15. In what time will $1600 amt. to $2000, at 8%?

16. What sum invested at 8% will yield an average income of $1560?

17. A man invests $15600, which gives him an annual income of $1014. What rate of interest does he receive?

18. What sum of money must be invested in real estate, yielding 10% profit in rents, to produce an income of $3370 ?

19. A note which had run 4 yr. 6 mo. amounted to $2000, at 7%. What was the principal?

20. B loaned $1600 at 6% until it amounted to $2000. What was the time?

21. I invest $35680 in a business that pays me a profit of $223 a month. What annual rate of interest do I receive?

The rate % per annum at which any sum will double itself may be found by dividing 100 yr. by the number of years.

22. At what rate will any number double itself in 16 yr.? In 12 yr.? In 8 yr. 4 mo. ? In 6 yr. 3 mo. ?

The time in years in which any sum will double itself may be found by dividing 100% by the rate %.

23. In what time will any number double itself, at 3% ? 41%? 5%? 6%? 7%? 8%? 10% ? 121% ?

24. In what time will the int. of any number at 8%, equal the principal? Twice the principal? One-half the principal ? 25. In what time will $9750 gain $780 int. at 2% a mo. ? 26. If I loan $750 at simple interest, and at the end of 1 yr. 3 mo. receive $843.75, what is the rate per cent?

27. If I receive $206.25 each quarter for rent of a house that cost me $15000, what rate % do I receive on the investment? 28. How large a sum in the savings bank, at 4% int., will give a yearly income of $1000?

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