It will be 17 times 6 cents, or 6 times 17, which is the same thing : $17 ,06 1,02 Answer; that is, 1 dollar and 2 cents. To find the interest on any sum for 1 year, it is evident we need only to multiply it by the rate per cent. written as a decimal fraction. The product will be the interest re. quired. What is the interest of $121 at 34 per cent. ? at 21 per cent. ? at 84 per cent. ? at 94 per cent. ? at 44 per cent. ? When we wish to obtain the interest for several years, we have only to multiply the interest of one year by the number of years. EXAMPLES. What is the interest of $214 for 4 years at 21 per cent ? for 3 yrs. ? for 9 yrs. ? for 24 yrs.? What is the interest of $364,41 for 8 yrs. at 64 per cent. ? What is the interest of $1000 for 120 yrs. ? Ans. $7200. It may often be needful to calculate the interest on a sum, for a less time than a year. When this is needful, the following mode is the most simple and expeditious. Let the interest be at 6 per cent, as that is the most common rate. At 6 per cent, each dollar gains 6 cents a year, (or 12 mo.) 6 cents for 12 mo. is b, a cent (or 5 mills) for 1 month. As 30 days is called a month, in calculating interest, 5 mills a month, is 1 mill for every 6 days. Interest at 6 per cent then gains on each dollar, $,06 a year. $,005 a month. $,001 for every 6 days, and of a mill for each day. Whenever therefore we wish to calculate the interest of any sum for less than a year, we can first calculate the in. terest on one dollar for the given time, calculating 5 mills for every month, 1 mill for every 6 days, and } of a mill for each odd day. After finding the interest for one dollar we can multiply this interest by the number of dollars in the sum. EXAMPLES. What is the interest of $36 at 6 per cent. for 9 mo. 12 days ? for 6 mo. 3 days ? for 8 mo. 18 days ? NOTE.-The fractions of a mill had better be changed to decimals. Thus instead of writing 51 mills we can write ,0055–54 mills can be written, ,0053+. (The sign of addition is added to the last because ther: are more deci. mal orders that may be added.) What is the interest of $334 for 4 mo. 2 d. ? for 9 mo. 6 d. ? for 7 mo. 4 d. ? What is the interest of $826 for 2 d. ? for 5 mo. 3 d.? for 16 d. ? for 9 mo. 16 d. ? If it is wished to obtain the interest of any sum for less than a year, at any other than 6 per cent. the method is, to find the interest at 6 per cent. and the take such parts of it, as the rate mentioned, is parts of 6 per cent. Thus if we wish to find the interest of $560 for 4 mo. 8 d. at 5 per cent. we first find the interest at 6 per cent. for that time, and then subtract i of the sum from itself. For the interest at 5 per cent. is į less than the interest at 6 per cent. Thus if the rate is 3 per.cent. we must take of the in. terest at 6 per cent. If it is 4 per cent. we must take 4 (or ) of the interest at 6 per cent., &c. What is the interest of $241,62 cents for 8 mo. 6 days, at 2 per cent. ? at 3 per cent. ? at per cent. ? at 9 per cent. ? at 124 per cent. ? at 15 per cent. ? What is the interest of $54.81 for 18 mo. at 5 per cent. ? Ans. 4.11. What is the interest of $500 for 9 mo. 9 days, at 8 per cent. ? Ans. $31.00. Wbat is the interest of $62.12 for 1 mo. 20 days, at 4 Ans. $0.345. What is the interest of $85 for 10 mo. 15 days, at 12} Ans. $9.295. per cent. ? per cent. ? RULES FOR CALCULATING INTEREST. To find the interest for years. Multiply the sum by the rate per cent. as a decimal of the order of hundredths, and the interest for one year is found. Multiply this answer by the number of years. To find the interest for months and days. Calculate the interest on one dollar for the given time, thus ; calculate 5 mills for every month, 1 mill for every six days, and į of a mill for each odd day. Add these together and multiply the answer by the number of dollars and cents in the sum, pointing off decimals according to rule. If the rate is any other than 6 per cent. calculate the inte. rest at 6 per cent., and then add to, or subtract from the sum such parts of itself, as the rate per cent. is parts of 6 per cent. EXAMPLES. Ans. $6,422 8,132 of 0,85 for 19 mo.? 0,08 9 0,909 5,737 of 8673 for 10 d. ? 14,455 of 0,73 for 10 mo.? ,036 What is the rule for calculating interest for one year? for a number of years ? for parts of a year? Rule for Sterling Money. When the principal is pounds, shillings, and pence, reduce the sum to the decimal of a £ (see page 180), and proceed as in federal money, The answer is in decimals of a £, and must be changed back to units (see page 181). What is the interest of £36 ; 9s. 6 d. for 1 yr. ? Ans. £2. 3s. 91 d. What is the interest of £36; 10s. for 18. mo. 20d. ? Ans. £3.8s. 13d. What is the interest of £95 for 9 mo.? Ans. £4.5s. 6d. Find the interest on £13; 3 ; 6 for 1 yr. ? A. 15s. 9 d. Find the interest on £13; 15s. 3 d. for 1 yr. 6 mo. A. £1; 4; 910. Find the interest on £75; 8; 4 for 5 yrs. 2 mo. A. £23.7s. 7d. Find the interest on £174 ; 10; 6 for 3 yrs. 6 mo. A. £36. 13s. Find the interest on £325; 12; 3 for 5 yrs. A. £97.13s. 8d. Find the interest on £150 ; 16; 8 for 4 yrs. 7 mo. A. £41.9s. 7d. VARIOUS EXERCISES IN INTEREST. TO FIND THE PRINCIPAL, WHEN THE TIME, RATE AND AMOUNT ARE KNOWN. If in 1 yr. 4 mo. the interest and principal on a sum at 6 per cent. amount to $61,02, what is the principal ? We first find what will be the amount of a dollar with its interest, for the given time. This amounts to $1,08. Now as every dollar in the original sum gained 8 cents interest, there were as many dollars as there are $1.08 in $61,02. $56,50. RULE. Find the interest of $1 for the given time and add to it. Divide the sum given by this amount. What is the rule for Sterling money? What is the rule to find the principal, when the time, rate, and amount are known? EXAMPLES. What principal at 8 per cent. will amount to $85,12 in 1 yr. 6 mo.? Ans. $76. What principal at 6 per cent. will amount to $99,311 in 11 mo. 9 d. ? Ans. $94. TO FIND THE PRINCIPAL, WHEN THE TIME, RATE, AND INTEREST ARE KNOWN. What sum put at interest at 6 per cent. will gain $10,50 in 1 yr. 4 mo. ? One dollar put at interest for that time, would gain $,08, and therefore it requires as many one dollars as there are 8,08 in $10,50. Ans. $131,25. RULE. Find the interest of $1 for the given rate and time. Di. vide the interest given by this, and the quotient is the prin. cipal. EXAMPLES. A man paid $4,52 interest at the rate of 6 per cent, at the end of 1 yr, 4 mo. what was the principal ? Ans. $56,50. A man received $20 for interest on a certain note at the end of 1 yr. at the rate of 6 per cent. what was the principal ? TO FIND THE RATE, WHEN THE PRINCIPAL, INTEREST, AND TIME ARE KNOWN, If $3,78 is paid for using $54, 1 yr. 6 mo. what is the rate per cent. ? If this sum were at interest at one per cent. it would produce 8,54. As many times therefore as $,54 is contained in $3,78 so much more than 1 per cent. is the rate. RULE. Divide the given interest by what would be the interest of the same sum at 1 per cent. How when time, rate, and interest are known? How find the rate, when principal, interest, and time are known? |