SECTION V.

INTEREST

Is of two kinds, Simple and Compound. Simple Interest is the sum paid by a borrower to a lender for the use of money lent, and is generally at a certain rate per cent. per annum, and is fixed by law, in several of the states, at 6 dollars for the use of 100 dollars for one year. Principal is the sum lent, bearing interest. Rate is the sum per cent. agreed on.

Amount is the principal and interest added together.

To find the interest of any sum for a year.

RULE. Multiply the principal by the rate per cent. and divide the product by 100, and the quotient will be the

answer.

Or say,

As $100 $6 :: $200 to $12 for a year.

EXAMPLES.

1. Lent a friend 150 dollars for a year; how much is he to give me for principal and interest, at the year's end, at

6

Ans. 159 dollars.

per cent.?

As 100 : 6 :: 150

:

$9 interest.

150 principal.

Ans. $159

2. How much is the interest of 125 dollars for one year, at 6 per cent. per annum ?

Ans. 7 dolls. 50 cts. 3. What is the interest of 400 dollars for two years, at

6 per cent. per annum ?

Ans. 48 dollars. 4. How much is the interest of 300 dollars for a year and a half, at 6 per cent. per annum ? Ans. 27 dolls.

5. What is the amount of 500 dollars for two years and a half, at 6 per cent. per annum ? Ans. 575 dolls.

6. How much is the amount of 1000 dollars for a year and a quarter, at 6 per cent. per annum ?

Ans. 1075 dollars. 7. What is the interest of 240 dollars for one year, at 5 per cent. per annum? Ans. 12 dollars. 8. Required the interest of 314 dollars for one year, at per cent. per annum ? Ans. 21 dolls. 98 cts.

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9. What is the amount of 560 dollars, due in one year, Ans. 604 dolls. 80 cts.

at 8 per cent. per annum ?

10. Required the interest of 760 dollars for one year, at 7 per cent. per annum ? Ans. 53 dolls. 20 cts.

When the time is more than one year.

RULE. Find the interest for one year, and multiply that by the number of years, and the product will be the answer.

11. What sum will discharge a debt of 250 dollars, due two years, at 6 per cent. per annum? Ans. 280 dolls.

12. Required the interest of 375 dollars for five years, at 7 per cent. per annum? Ans. 131 dolls. 25 cts.

When the principal is dollars and cents, or dollars, cents and mills, and the time years only.

RULE. Multiply the given sum by the rate per cent. and divide the product by 100, and the quotient will be the answer in the same name with the lowest denomination in the principal, for one year only; but if for two or more years, multiply the interest found for one year by the number of years, and that product will be the answer.

13. What is the interest of 250 dollars 50 cents for one year, at 6 per cent. per annum? Ans. 15 dolls. 3 cts. 14. Required the amount of the above sum for four years, at 7 per cent. per annum? Ans. $20 dolls. 64 cts. 15. What is the amount of a note for 800 dolls. 75 cts. due five years, at 8 per cent. per annum ?

Ans 1121 dollars 5 cents. 16. What sum will discharge a bond of 630 dolls. 50 cts. on which there is five years interest due, at 8 per cent. per annum? Ans. 882 dollars 70 cents.

17. How much is the interest of 325 dolls. for three years, Ans. 58 dolls. 50 cts.

at 6 per cent. per annum?

18. What is the interest of 173 dollars 50 cents for two years, at 6 per cent. per annum ?

Ans. 20 dollars 82 cents.. 19. What is the interest of 279 dollars 87 cents for two years and a half, at 7 per cent. per annum ?

Ans. 48 dollars 97+ cts. 20. What is the interest of one dollar for one year, at 6 per cent. per annum ?

Ans. 6 cents.

21. What sum will discharge a bond for 500 dollars 50 cents, due four years and a half, at 7 per cent. per annum? Aug. 658 dollars 15 cents 7+ mills.

When the principal is dollars, cents, &c. the time years and months, or months only, and when the rate per cent. contains a fraction, as 4,,, &c.

RULE. Multiply by half the number of months in the given time, when the rate is at 6 per cent. per annum; but if the given rate be more or less than 6 per cent. multiply the given number of months by the rate, and divide the product by 12, and the quotient will be the rate for the time. The principal multiplied by this rate will give the interest required; and when the fraction occurs, you must multiply the principal by the fraction, as well as the whole number, and add it in.

22. How much is the interest of 187 dollars 25 cents for 1 year 4 months, at 6 per cent. per annum?

Ans. 14 dollars 98 cents. 23. What is the interest of 341 dollars 52 cents for 7 months, at 6 per cent. per annum ?

Ans. 12 dollars 80 cents 7 mills. 24. What is the interest of 400 dollars 50 cents for 2 years 8 months, at 7 per cent. per annum ?

6 per cent. per annum?

Ans. 80 dollars 9 cents 9 mills.

25. What is the interest of 342 dollars for 11 months, at Ans. 18 dolls. 81 cts. 26. What is the interest of 95 dollars for two months, at Ans. 95 cents.

6 per cent. per annum?

27. How much is the amount of 250 dollars 80 cents for 18 months, at 83 per cent. per annum?

Ans. 283 dollars 71 cents 7 mills. 28. What is the interest of 694 dollars 84 cents for nine months, at 10 per cents per annum ?

Ans. 52 dollars 11 cents 3 mills. 29. How much is the amount of 985 dollars for 5 years 8 months, at 6 per cent. per annum ?

Ans. 1319 dollars 90 cents. 30. What is the amount of 1260 dollars for four months, at 6 per cent. per annum ? Ans. 1287 dolls. 30 cts. 31. What is the amount of 240 dollars for 15 months, at cent. per annum? Ans. 262 dollars 50 cents.

71 per

When the principal is dollars, cents, &c. and the time is months and days, or days only.

RULE. Find the interest for the given months by the last rule, and take aliquot parts for the days; or multiply the given sum by the number of days, (when the rate is 6 per cent.) and divide the product by 60, and the quotient will

be the answer required. In taking aliquot parts for days, the calculation is made at 30 days to a month. By this method of taking aliquot parts for days, it is not exactly sufficient, where there is a large sum to be calculated; but on small sums the difference is very small. The correct way is to find the interest for the months, and then, by the Rule of Three, say, as 365 days is to the interest for one year, so is the number of days to the interest they will bring, which, added to the interest found for months, will give the answer.

32. What is the interest of 194 dollars for 4 months 12 days, at 6 per cent. per annum?

Ans. 4 dollars 26 cents 8 mills. 33. Required the interest of 640 dollars 60 cents for 100 days, at 6 per cent. per annum?

Ans. 10 dollars 53+ cents. 34. What is the amount of 481 dollars 75 cents for 25 days, at 7 per cent. per annum ?

Ans. 484 dollars 5 cents 9+ mills. 35. What is the amount of 564 dollars for 44 days, at 6 per cent. per annum? Ans. 568 dolls. 7cts. 9+ m.

36. What is the interest of 87 dolls. 56 cts. for 72 days, at 6 per cent. per annum? Ans. 1 dol. 3 cts. 6 m. 37. What is the amount of 8400 dollars for 20 days, at 5 per cent. per annum ? Ans. 8423 dollars. 38. How much is the amount of 298 dolls. 59 cts. from the 19th May, 1826, to the 11th August, 1827, at 8 per cent. per annum? Ans. 327 dollars 98 cents 4 mills. 39. How much interest is due on a note, passed the 14th of June, 1827, for 196 dollars, at 5 per cent. per annum, on the 14th of December following?

Ans. 4 dolls. 90 cts.

40. Required the amount of 73 dollars 41 cents for 27 days, at 6 per cent. per annum? Ans. 73 dolls. 74 cts.

at 6 per cent. per annum?

41. How much is the interest of 35 dollars for 256 days, Ans. 1 dol. 47cts. 2 m. 42. How much is the amount of 455 dollars 52 cents for 47 days, at 6 per cent. per annum ?

Ans. 459 dollars 3 cents 9 mills.

NOTE. Work the above questions by the Double Rule of Three Direct.

When the amount, rate and time, are given to find the principal.

RULE. As the amount of 100 dollars, at the rate and time given, is to 100 dollars, so is the amount given to the principal required.

43. What principal put to interest for eight years, at 6 per cent. per annum, will pay a debt of 1000 dollars?

44. What sum being put to interest for twelve years, at 7 per cent. per annum, will amount to 626 dolls. 6 cts.? Ans. 340 dolls. 25 cts.

45. What sum put to interest for five years, at 6 per cent. per annum, will amount to 728 dollars? Ans. $560. 46. Received 700 dollars as payment in full for a note with four years interest due thereon, at 6 per cent. per an

num. How much does the note call for?

Ans. 564 dollars 51 cents 6 mills.

When the amount, time and principal, are given to find the rate.

RULE. As the principal is to the interest for the whole time, so is 100 dollars to its interest for the same time. Divide the interest so found by the time, and the quotient will give the rate per cent.

47. At what rate per cent. will 340 dollars 25 cents amount to 626 dollars 6 cents in twelve years?

$ cts. 626 6

340 25

As 340 25: 285 81 :: 100 : 84127 per cent. Ans.

48. At what rate per cent. will 675 dolls. 67 cts. 534 m. amount to 1000 dollars in eight years? Ans. 6 per cent. 49. Paid 728 dollars in full for a note of 560 dollars, with five years interest due thereon. What was the rate per cent. per annum? Ans. 6 per cent.

50. At what rate per cent. will 500 dollars amount to 725 dollars in nine years? Ans. 5 per cent.

51. At what rate per cent. will 1260 dollars amount to 1638 dollars in four years? Ans. 7 per cent.

When the principal, amount and rate, are given to find the time.

RULE. Find the interest of the given sum for one year, and then say, as the interest for one year is to one year, so is the interest of the whole sum to the time required.