340. Those who prefer can use the following method of

341. Hence, to find the interest of $1 at 6% for any

time,

Take 6 cents for each year, 1 cent for each 2 months in the part of a year, 5 mills for the odd month, and 1 mill for each 6 days in the part of a month.

342. Oral Exercises.

67. What is the interest of $1 for 3 yr. 9 m. 18 d. ?

Solution. The interest of $1 for 3 years is 18 cents; for 9 months is 4 cents and 5 mills; for 3 yr. 9 m., therefore, it is 22 cents and 5 mills; for 18 days it is 3 mills; therefore, for 3 yr. 9 m. 18 d. it is 22 cents and 8 mills, or $0.228, Ans.

68. What is the interest of $1 for 2 yr. 5 m. 20 d. ? 69. What is the interest of $1 for 3 yr. 1 m. 15 d. ? 70. What is the interest of $1 for 1 yr. 3 m. 29 d.? 71. What is the interest of $1 for 4 yr. 2 m. 4 d.? 72. What is the interest of $1 for 4 yr. 3 m. 17 d.? 73. What is the interest of $1 for 4 yr. 9 m. 12 d. ? 74. What is the interest of $1 for 10 yr. 11 m. 7 d.? 75. What is the interest of $1 for 2 yr. 11 m. 5 d. ? 76. What is the interest of $1 for 1 yr. 8 m. 3 d. ?

343. Written Exercises.

77. What is the interest of $ 256 for 1 yr. 5 m. 12 d.? What is the amount?

344. To find the interest of any sum at 6 % for any time,

Rule.

Multiply the principal by the decimal which expresses the interest of $1 at 6% for the given time.

345. To find the amount,

Add the principal to the interest. Or,

Multiply the principal by the decimal which expresses the amount of $1 at 6% for the given time.

For examples, let this method be applied to those already given, pages

180-185.

EXACT INTEREST.

346 In the methods given for finding the interest for months and days, 30 days have been counted a month, and 12 months, or 360 days, a year (Art. 336). By these methods the computed interest of 360 days, that is, of 38g, or of a year, is the interest of a full year. computed interest for any number of days is too great.

Thus, the

of itself

347. To find the exact interest for any number of days,

Rule.

Find the interest for the exact number of days as in the common method, and decrease it one seventy-third of itself. Or,

Multiply one year's interest of the principal at the given rate by the exact number of days, and divide the product by 365.

NOTE 1. In England and in dealings with the United States Government exact interest is computed.

78. What is the exact interest of $438 from Feb. 12, 1894, to May 8, 1894 ?

79. What is the exact interest of $256.15 from May 17 to July 31, 1895 ?

80. Find the amount at exact interest of $57.38 at 7 % from Sept. 18 to Dec. 13, 1895.

81. What is the amount of $187.44 from May 25, 1893, to April 19, 1895, at 7% %, exact interest?

NOTE 2. The exact interest at 7% is 2 cents a day for every $100.

PROBLEMS IN INTEREST.

348. In every example in interest there are four elements, viz. Principal, Rate, Time, and Interest, any three of which being given, the other can be found.

349. Principal, Interest, and Time given, to find the Rate.

82. At what rate must $ 300 be put on interest to gain $18 in 2 years?

Solution. $300 at 1% will gain $6 in 2 years. Therefore, to gain $ 18, the rate must be the quotient of $18÷$6=3; 3%, Ans. Hence,

Rule.

Divide the given interest by the interest of the principal, for the given time, at 1 per cent, and the quotient will be the

83. At what rate must $142 be put on interest to gain $ 21.30 in 3 years? Ans. 5 %.

84. If $36 gain $ 7.56 in 3 years, what is the rate? 85. If $300 gain $ 43.80 in 2 years, what is the rate? 350. Amount, Time, and Rate given, to find the Principal. 86. What principal, at 5 %, will amount to $110 in 2 years? Solution. $1 in 2 years at 5 % amounts to $1.10. Therefore, the principal must be the quotient of $ 110 ÷ 1.10=$100, Ans. Hence,

Rule.

Divide the given amount by the amount of $1 for the given rate and time, and the quotient will be the principal.

87. What principal at 6 % will amount to $130.39 in 8 months? Ans. $125.375.

88. What principal at 8 % for 3 years will amount to $74.40? 89. What is the interest for 2 yr. 6 m. at 8% of that sum which will, at the given rate and time, amount to $240?

351. The Present Worth of a debt, payable at a future time without interest, is a sum of money which, put at legal interest, will amount to the debt at the time of its becoming due.

352. The debt, then, is an amount, the present worth is the principal, that is, we have the amount, time, and rate given to find the principal. The interest on the principal is called the discount.