5. What is the interest of $325.00 for 3 years at 6 pr. ct.?

Ans. $58.50.

6. What is the interest of $233.00 at 5 pr. ct. for 7 years? Ans. $81.55.

7. What is the interest of $647.33 at 6 pr. ct, for 8 years? 8. Find the interest on $2,345.65 at 7 pr. ct. for 9 years. 9. What is the amount of $500.00 at 6 pr. ct. for 4 ? years Ans. $620.

NOTE. The amount may be found by adding the principal to the interest, or by adding a unit to the rate before multiplying. (§LXXIV.) 10. What is the amount of $850.00 for 5 years at 6 pr. ct.?

A. $1,105.

11. What is the amount of $1,000 at 7 pr. ct. for 8 years?

A. $1,560.

12. What is the amount of $1,275.63 for 9 years at 5 pr. ct.? 13. What is the amount of $9,653.61 for 10 years, at 6 pr. ct.? 14. What is the amount of $11,943.11 for 11 years, at 8 pr. ct.?

§ LXXVII. MONTHS. It will be observed that when the time is a number of even years, it is as easy to calculate interest at one rate as at another; since the rule is the same for all. Whatever be the rate pr. cent., then, if the time be even years, let the pupil proceed as in the last section. But when there are months and days, 6 pr. ct. is the easiest rate. In the following examples then, 6 per. ct. may be understood, unless another rate be expressed. Particular rules will, afterwards, be given, for calculating interest at different rates.

MENTAL EXERCISES.

1. If the rate for a year (12 months) be 6 pr. ct., what ought it to be for half a year, that is for six months?

2. If the rate for 6 months be 3 pr. ct., what ought it to be for 2 months?

3. If the rate for two months be 1 pr. ct., what ought it to be for 4 months? What for 8 months? What for 10 months?

4. If the rate for 2 months be 1 pr. ct. what ought it to be for 1 month? For 3 months? For 5 months? For 7 months? For 9 months? For 11 months?

Here the pupil will observe, that the rate per ct. is always just half the number of months. The same is true if we go above a year, thus,

5. If the rate for 2 months be 1 pr. ct., what is that for 14 months? For 16 months? For 18 months? For 20 months?

6. If the rate for 1 month be pr. ct., what is that for 13 months? For 15 months? For 17 months? For 19 months?

Hence, when interest is at 6 pr. ct. pr. an.,

THE RATE FOR ANY NUMBER OF MONTHS, IS HALF THE NUMBER OF MONTHS.

Let the following be written.

1. What is the interest on $98.75 for 2 months? Half of 2 months is 1 month.

1 pr. ct. then, is the rate.

98.75X.01

$0.9875 Ans.

A. $0.83325.

2. What is the interest on $29.25, for 4 months? Half of 4 is 2. Therefore the rate is 2 pr. ct. Ans. $0.585. 3. Find the interest on $33.33 for 5 months. NOTE. In practice, neglect the decimals of a mill if under .5 or a mill; if equal to or over, add another mill instead of them. Or, rather, men in business usually neglect the mills, if under half a cent, if equal to or over, they add another cent instead of them. This is only to be done in the final result.

If done bofore multiplying, it will make too great an error. In the examples, thus far given, however, the decimals have been retained, in order to insure perfect accuracy in the operations.

4. What is the interest on 72.05 for 3 months? Half of 3 is 1. Therefore the rate is 1 pr. ct.=.015. A. $1.08075. 5. What is the interest on $294.63 for 6 months? A. $8.8389. 6. Find the interest on $765.23 for 7 months. A. $25.78305. 7. Find the interest on $895.64 for 8 months. A. $35,8256. 8. Find the interest on $934.31 for 9 months. 9. Find the interest on $1.853.63 for 10 months. 10. Find the interest on $3.293 for 11 months. 11. Find the interest on $7.86345 for 11 months. NOTE. The pupil may, in the examples which follow, multiply by the rules given in § LXIII., Multiplication of decimals, retaining decimals only to three places, or mills. The nearest mill is usually given in the answer.

A. $0.703
A. $4.273

12. What is the interest of $243.23 for 14 months? A. $17.026 13. What is the interest of $147.96 for 6 months? A. $4.439 14. Find the interest on $15.125 for 11 months. A. $0.832 15. Find the interest on $28.14 for 5 months. 16. Find the interest on $284.85 for 3 months. 17. Find the interest on $396.27 for 7 months. 18. Find the interest on $19.395 for 9 months. 19. Find the interest on $1,288.91 for 10 months. 20. Find the interest on $2,956.84 for 11 months.

21. What is the interest on $37.00 for 2 years and 4 months? In this example, we may either reduce the whole time to months, and find the rate by taking half, as usual; or we may find the rates for the years and months separately, and add them together. The latter mode is best, when the number of years is great.

Rate for 2 years =2.06.12; for 4 months .02 .12+.02= .14, rate for the whole time. Ans. $5.18.

22. Find the interest on $834.31 for 3 years and 8 months.
Ans. 183.5482.

23. Find the interest on $976.24 for 5 years and 7 months.
24. Find the interest on $631.874 for 9 years and 9 months.
25. What is the amount of $8,600, for 6 yrs. 6 mo. ?
26. What is the amount of $5,837.29, for 19 yrs. 11 mo. ?

§ LXXVIII. DAYS. To a pupil, the calculation of interest for odd days, as they are called, is usually perplexing. We hope to make it clear. In calculating interest, 30 days are reckoned to the month, and 12 months to the year. This is slightly erroneous, but custom has rendered it almost universal. It will be seen, that this mode of allowance makes the year to consist of only 360 days. For ordinary purposes, however, it is sufficiently accurate; and its convenience renders it general.

MENTAL EXERCISES.

1. If the rate for 2 months be 1 pr. ct., that is, if the rate for 60 days be 1 pr. ct., what is that for 6 days? NOTE. 6 days=60÷÷10= of 60 days. A.

pr. ct. 2. If the rate for 6 days be pr. ct., what is that for 12 days? For 18 days? For 24 days? For 30 days? For 36 days? For 42 days? For 48 days? For 54 days. 3. What is the rate pr. ct. for 2 months and 6 days? NOTE. For 2 months, it is 1 pr. ct., and for 6 days Ans. 1 pr. ct. pr. ct. 4. What is the rate for 2 months, 12 days? 18 d.? For 2 mo. 24 d.? For 2 mo. 36 d.?

18 d.? For 4 mo. 24 d. ?

For 2 mo.
For 4 mo.

5. What is the rate for 6 mo. 6 d. ?. For 6 mo. 12 d. ? For 8 mo. 18 d.?

6. What is the rate for 8 mo. 6 d.? For 12 mo. 18 d. ?

For 1 yr. 24 d. ?

pr.

It will be observed, that for once 6 days we have ct.; for twice 6 days, we have pr. ct.; for three times 6 days, we have pr. ct. &c. Now pr. ct. is .001 ;

( LXXIV.) is .002; is .003, and so on. Hence, for every 6 days we have one thousandth in the rate.

If there be fewer days than 6, as 3 days, we shall have a part of a thousandth, that is, in this case, a thousandth =.0005. If the days be 2, we shall have }=} of a thousandth; =.0003; if 4, = of a thousandth = .0006; if 5, § of a thousandth =.00083; if 1, † of a thousandth =.00016. Hence, to find the rate decimally for any number of days.

DIVIDE THE DAYS BY 6, ANNEXING CYPHERS, IF NECESSARY, AND PUT THE FIRST FIGURE OF THE QUOTIENT IN THE THOUSANDTHS' PLACE, WHEN

THE DAYS ARE 6 OR MORE, IN THE TEN THOUSANDTHS' WHEN THEY ARB UNDER 6.

Thus, for the rate for 23 days; 23÷6=383. As the days are over 6, put the first figure 3 in the thousandths' place, thus, .00383. The rate for two days is found, thus; 2÷6=3. As the days here are under 6, the quotient must begin in the ten thousandths' place, thus .0003. In these cases the cyphers, though not written, were supposed to be annexed.

EXAMPLES FOR PRACTICE.

1. What is the interest of $100.00 for 2 mo. 6 d. ? A. $1.10. Rate for 2 mo.. =.01 For 6 d.=.001. Rate for the whole time =.011.

2. Find the interest on $600.00 for 4 mo. 18d. A. $13.80. Rate for 4 mo.-.02. For 18 d.=.003. Rate for whole time =.023.

3. Find the interest of $800.00 for 6 mo. 21 d. A. $26.80. Rate for 6 mo.-.03. For 21 d.=.0035. Rate for whole time =.0335.

4. Find the interest on $9,000.00 for 8 mo. 4 d. A. $366.00. Rate for 8 mo.-.04. For 4 d.=.0006. For whole time=.0406. 5. Find the interest on $127.47 for 2 mo. 12 d. A. $1.53— 6. Find the interest on $115.42 for 7 mo. 15 d. A. $4.328+ 7. Find the interest on $143.18 for 1 yr. 7 mo. 14 d. A$13.936Rate for 1 yr.=.06. For 7 mo.-.035. For 14 d.=.0023. For whole time=.0973.

NOTE. We would here mention, that when the rate repeats, or is a long decimal, the vulgar Fraction may be retained. This will often be most convenient, and convenience should decide the question. Thus, instead of using the decimal .0973, we would recommend the use of .0973. This is likewise perfectly accurate, whereas, when the repetend is used, perfect accuracy cannot be obtained, by the common mode of multiplying.

8. Find the interest on $625.00, for 3 yrs. 2 mo. 7 d.

A. 119.479. Rate for 3 yrs.=.18. For 2 mo. =.01. For 7 d. .001. For whole time.191.

9. Find the interest on $930.00 for 6 yrs. 3 mo. 11 d.

Ans. $350.455.

10. Find the interest on $865.25 for 9 yrs. 4 mo. 15 d. NOTE. When the months are even, and the days are an aliquot, or an even part of 2 months or 60 days, it is well to make a vulgar Fraction for the days instead of a decimal. For example, if, as in the last question, there are 15 days, this will be of 60. Now the rate for 60 d. or 2 mo. is .01. Therefore the rate for 15 d. is of .01 .04. This will often save figures. Then, in the last question, the rate for 9 yrs..54, for 4 mo.-.02, for 15 d.=.04, for the whole .56. Ans. $486.703.

11. Find the interest of $750.00 for 12 yrs. 3 mo.

NOTE. The learner will readily see that an odd month, being of 2 months, may have .04 as its rate. Then, in the last example, rate for 12 yrs.=.72, for 3 mo.-.01, whole rate =.734. Ans. $551.25.

These abbreviations are only suggested, and if they do not seem clear, the pupil is recommended to follow the general mode. Other vulgar Fractions may sometimes be conveniently used, which we leave the pupil to discover. Hence, the general rule for calculating interest seems to be

FIND THE DECIMAL RATES FOR YEARS, MONTHS AND DAYS SEPARATELY, ADD THEM TOGETHER, AND MULTIPLY THE PRINCIPAL BY THEIR SUM. 12. Find the interest on $725.34 for 16 yrs, 6 mo. 12 d. NOTE. 12 d. is of 60 d. Hence the rate is .99.

13. Find the interest on $348.31 for 11 yrs. 8 mo. 10 d. 14. Find the interest on $795.333 for 13 yrs. 9 mo.

15. Find the interest on $5,863.63 for 7 yrs. 11 mo.

16. Find the interest on $325,965.813 for 15 yrs. 8 mo. 20 d.

17. A note was given with interest, for $2,635.00, on the 17th of February, 1827, and paid on the 12th of March, 1830. What was the interest due, and what was the amount of the note?

A. Int. $485.2791. Am. $3,120.279.

NOTE. In this example we are obliged to find the time. In business, we are almost always under the necessity of doing this. It may be done by Subtraction of Compound numbers, (§XXXVII.) The greater number consists of 1830 2 months, (Jan. and Feb.) and 12 days, (in March.) The less, consists of 1827 years, 1 month, (Jan.) and 17 days, (in Feb.)

Set down the numbers, thus,

In subtracting, disregard entirely the inequality of the months, and call them all 30 days, allowing 12 months to the year. If interest be required for days exactly, the inequality of months must be taken into account, (see § LXXIX.)

years,

Yrs. mo. d.

1830; 2; 12 1827; 1; 17

3; 0; 25

18. A note was given with interest, for $1,143.16 on the 9th of August, 1826, and paid on the 16th of April, 1830. What was the amount of the note, when paid? A. $1,395.989

19. A note was given, with interest, for $6,325.13 on the 8th of October, 1823, and paid on the 11th of August, 1829. What was then due ?

20. A note was given, with interest, for $2,647.53, on the 27th of December, 1821, and paid on the 15th of November, 1828. What was then due ?

21. A note was given for $15,833.75, on the 8th of July, 1819, and paid, with interest, on the 11th of June, 1827. What was then due ?

22. A note was given on the 23d of March, 1813, and paid, with interest, on the 17th of September, 1830. The note was for $12,981 .375. What was due at the time of payment?

23. A note continued accumulating interest for 50 years, 9 mo. 3 d. It was given for $25,864.29. What was the interest? What was the amount?

24. A note of $30,329.18, lay on interest from July 19th, 1763, to August 17th, 1829. What did it amount to ?

§ LXXIX. In BANKS, notes are usually written for a certain number of days, as 30 days, 60 days, 95 days, &c. Sometimes, also, but not in Banks, interest is calculated for years and days, without regard to months,