3. The interest on $1800 for 4 yr. 8 mo. 16 da. is $424. What is the rate?

4. At what rate will $2460 give $682.65 interest in 5 yr. 6 mo. 18 da.?

5. A note for $880 was given July 5, 1900, and settled May 2, 1904, for $1081.96. What rate per cent was charged? Finding the time.

Written Work

1. In what time will $450 at 6% yield $90 interest?

Since the interest on $450 for 1 yr. at 6% is $27, the required time is as many years as $27 is contained times in $90, or 33 yr.

The time in years equals the given interest divided by the interest at the given rate for 1 year.

2. In what time will $275 gain $55 interest at 6%?

3. In what time will any principal double itself (that is, gain 100% of itself) at 5%? at 6%? at 8% ?

4. In what time will any principal treble itself (that is, gain 200% of itself) at 5%? at 6%? In what time will it quadruple itself at 8% ? at 10%?

5. A note of $500 at 5% interest was paid May 1, 1905, the interest amounting to $63.75. When was the note given?

REVIEW PROBLEMS

1. Find the interest on $80 for 6 yr. 6 mo. 18 da. at 6%. 2. In what time will $180 at 5 % yield $22.50 interest? 3. In what time will $600 amount to $715.50, at 51% interest?

4. At what rate will $1650 gain $326.70, in 4 yr. 4 mo.

24 da.?

5. What sum of money loaned at 6% will give a semiannual income of $13.02?

6. Interest $31.80; time 3 yr. 6 mo. 12 da.; rate 5%. Find the principal.

7. The interest of of a principal for 3 yr. 6 mo. at 6% is $19.25. Find the principal.

8. If $186 pays a debt of $150 which has been due for 4 years, what is the rate of interest?

9. I borrowed $450 at 5% and kept it until it amounted to $525. When did I settle the note ?

10. Dec. 1, 1901, I loaned $300 at 51%. Find the amount due March 16, 1905.

11. Find interest at 6% on $350 from June 1, 1898 to Aug. 13, 1902.

12. If $300 was borrowed April 1, 1902, at 5%, when should the principal and interest be paid that their sum may be $357?

13. The amount of a certain principal at 6% for a given time is $780, and at 10% for the same time it is $900. Find the principal.

14. If $148 is loaned April 1, 1902, at 5%, when will it amount to $179.45?

15. What principal for 3 mo. at 8% will amount to the interest on $ 5100 for 5 yr. 8 mo. at 6% ?

16. A farmer bought 75 acres of land at $50 an acre, paying cash, and giving his note for the balance, due in 3 yr. 6 mo., with interest at 6%. What was the amount of the note at maturity?

ANNUAL INTEREST, OR SIMPLE INTEREST ON UNPAID INTEREST

In some states when a note reads with interest " payable annually," simple interest may be collected upon the principal and upon each year's interest from the time it was due until paid.

In most states annual interest is not collectable by law.

Interest payable annually is simple interest; but interest collected on the principal and on the overdue payments of simple interest is annual interest.

Written Work

1. James Brown borrows $1200 at 6% interest, "payable annually." In case no interest is paid for 3 years, 6 months, and 15 days, how much money is necessary to pay the debt?

Simple interest on $1200, at 6%, for 3 yr. 6 mo. 15 da.
The interest for each year is $72.

The 1st annual int., $72, remains unpaid for 2 yr. 6 mo. 15 da.
The 2d annual int., $72, remains unpaid for 1 yr. 6 mo. 15 da.
The 3d annual int., $72, remains unpaid for

Interest on $72 at 6% for

6 mo. 15 da.

255

274 98

1200 00

1474 98

The annual interest on $1200 for 3 yr. 6 mo. 15 da.
The principal

The amount of $1200 at annual interest for 3 yr. 6 mo. 15 da.

Annual interest is the simple interest on the principal for the given time plus the simple interest on each year's interest for the time it remains unpaid.

2. Find the total interest due on a note of $675 for 2 years, 8 months, and 20 days at 6%, with interest payable annually, if no interest has been paid.

3. Find the amount of $6400 for 4 years, 5 months, and 15 days, with interest payable annually at 6 %.

4. An attorney collects a note of $3750 with annual interest on it at 6% for 4 yr. 9 mo. 18 da. Find the amount collected and his commission on it at 10%.

EXACT INTEREST

Exact interest is simple interest on the principal reckoned on the basis of 365 days to a common year and 366 days to a leap year.

It is used in computing interest on all obligations by the United States government; on all foreign securities; and to some extent by city controllers and bankers.

Since common interest is computed on the basis of 12 months of 30 days each, or 360 days; and exact interest is reckoned on the basis of 365 days to a common year, or 366 to a leap year, 1 day's exact interest is of a year's common interest.

It is evident that the common and exact interest for 1 year are the same. Thus, of one year's common interest equals one year's exact interest. They differ only for parts of a year.

Written Work

1. Find the exact interest on $2400 for 95 days at 6%.

Exact interest for 1 year = 6% of $2400, or $144

Exact interest is found by dividing the common interest at the given rate for one year by 365 and multiplying the quotient by the exact number of days.

6. $500 for 90 days at 9%.
7. $1020 for 74 days at 10%.
8. $6500 for 280 days at 6%.

Find the exact interest of: 2. $800 for 78 days at 6%. 3. $2000 for 92 days at 7%. 4. $2400 for 115 days at 8%. 5. $1775 for 100 days at 81%. 9. $10000 for 61 days at 7%.

10. Find the exact interest on $1020 from Oct. 19, 1905 to April 1, 1907, at 6%.

NOTE.-Why do we find exact interest for a fraction of a year only? The exact number of days from Oct. 19, 1905 to April 1, 1907, is found as follows: Oct., 12 da.; Nov., 30 da.; Dec., 31 da.; Jan., 31 da.; Feb. 28 da.; March, 31 da.; April, 1 da. Total, 164 days.

11. Find the exact interest on $1795.80 from July 7, 1904 to Sept. 1, 1907 at 7%.

12. The United States government paid exact interest at 4% on a warrant of $650000, 83 days past due. Compute the amount paid.

COMPOUND INTEREST

Mr. Reed Colburn loans Robert Patterson $200 for 2 years at 6%.

Suppose Mr. Patterson says to Mr. Colburn, at the end of the first year: "I cannot pay you the $12 interest due, but will pay you interest at 6% on the $12 for a year." How much interest should Mr. Patterson pay Mr. Colburn at the end of the 2 years? How does the $24.72 interest differ from simple interest?

Compound interest is interest on both the principal and the unpaid interest added to the principal when due.

Interest may be added to the principal annually, semiannually, or quarterly, according to agreement.

Written Work

1. Find the compound interest on $200 for 2 years 6 months at 6%.