Example 1. What is the interest on $350 at 8% for 2 mo. 18 da.? Solution. 1. Since 8%=6%+2%, first find the interest at 6% and add to that one third of itself, because 2% of 6%. 2. The interest on $1 at 6% for 2 mo. 18 da. = $.013. 3. 4. the interest on $350 at 6% for 2 mo. 18 da. = 350 ×$.013 = $4.55 ..the interest on $350 at 2% for 2 mo. 18 da. X$4.55 1.516 5. the interest on $350 at 8% for 2 mo. 18 da. (adding) = = $6.066, or $6.07 Example 2. What is the interest on $275 at 7%, borrowed on January 10 and repaid on May 7? Solution.—1. From Jan. 10 to Apr. 10 is 3 mo.; from Apr. 10 to Apr. 30 is 20 da.; from Apr. 30 to May 7 is 7 da. Hence the total time is 3 mo. 27 da. 2. The interest on $1 at 6% for 3 mo. 27 da. = $.0195. 3. ..the interest on $275 at 6% for 3 mo. 27 da. =275×$.0195=$5.36 . the interest on $275 at 1% for 3 mo. 27 da. 5. ..the interest on $275 at 7% for 3 mo. 27 da. 4. EXERCISE 18 = of $5.36 .89 (adding) = = $6.25 1. Suppose that the rate of interest in Example 2 above had been 5%. What would you do in step 5 of the solution to find the interest? 2. Suppose that the rate of interest in Example 1 above had been 4%. What would you do in step 5 of the solution to find the interest? 3. What part of the interest at 6% is interest at 3%? How will you find the interest at 9% when you have found the interest at 6%? 4. Find the interest for 8 mo. on $500 at: a. 6%; b. 3%; c. 2%; d. 1%. 5. Find the interest on $750 for 4 mo. 18 da. at: a. 6%; b. 1%; c. 5%; d. 7%. 5. Find the interest on $950 for 5 mo. 12 da. at: 7. Find the interest on $1350 for 3 mo. 24 da. at: 8. Find the interest on $2300 for 9 mo. 6 da. at: 9. Find the interest on $500 at 8% borrowed on March 10 and repaid on May 22. 10. Find the interest and the amount due at 7% on $600 borrowed on May 16 and repaid on June 22. 11. Find the interest and the amount due at 5% on $2500 borrowed on August 12 and repaid on November 8. 12. Find the interest and the amount due at 7% on $375 borrowed on March 11 and repaid on June 8. 13. Find the interest and the amount due at 8% on $750 borrowed on December 7, 1921, and repaid on February 25, 1922. 14. Find the interest and the amount due at 7% on $1250 borrowed on September 14, 1921, and repaid on November 26, 1921. 15. Find the amount due at 8% on $825 borrowed on August 25 and repaid on October 18. NOTE. Interest at many other rates can be found either in this same manner or by means of a simple interest table. A list of examples involving some rates which are actually found in business transactions, but not commonly, is printed on page 244. A simple interest table and the method of using it are explained in Section 18, page 38. These are, however, supplementary topics, to be studied only if the teacher decides that the class have time for them. Topic B.Compound Interest 15. When interest earned on money during an interest period (like three months, or six months) is added to the principal and, with it, draws interest during the next interest period, the money is said to earn compound interest and the final amount due is called the compound amount. If the interest is computed and added every three months, it is said to be compounded quarterly; if every six months, then it is compounded semi-annually; etc. Example. -What is the compound amount and the compound interest on $400 invested for 2 yr. at 6% compounded semi-annually? Solution. = 1. The interest for the first 6 mo. 3% of $400 6. 7. 8. = $450.20-$400 = $50.20 for 2 yr. = $48. NOTE 1. The simple interest on $400 at 6% The difference between the simple interest and the compound interest becomes greater as the length of time becomes greater. NOTE 2. In the following examples, carry out all computations to four decimal places, but express the final results to only two places. EXERCISE 19 1. If the annual rate of interest is 6%, what is the semi-annual rate? What is the quarterly rate? 2. If the annual rate of interest is 4%, what is the semi-annual rate? What is the quarterly rate? 3. a. Find the compound amount and the compound interest on $500 invested at 6% compounded annually for 3 yr. b. What is the simple interest on $500 at 6% for 3 yr.? c. How much more than the simple interest is the compound interest? 4. a. Find the compound amount and the compound interest on $250 invested at 5% compounded annually for 4 yr. b. What is the simple interest on $250 at 5% for 4 yr.? 5. Find the compound amount and the compound interest on $300 invested at 4% compounded semiannually for 3 yr. 6. Find the compound amount and the compound interest on $750 invested at 6% compounded semiannually for 4 yr. 7. Find the compound amount and the compound interest on $825 invested at 4% compounded quarterly for 3 yr. 8. Find the compound amount and the compound interest on $400 invested at 6% compounded semiannually for 2 yr. and 6 mo. 9. What is the compound interest on $600 invested at 4% compounded quarterly for 3 yr.? 10. What is the compound interest on $600 invested at 4% compounded semi-annually for 3 yr.? 16. A compound amount table is usually employed to get compound interest. A short table is given below. This table gives the compound amount of $1 invested at 4% compounded quarterly, semi-annually, and annually for one year to ten years inclusive. Much more extensive tables are needed and can be obtained. TABLE GIVING THE COMPOUND AMOUNT OF $1 INVESTED AT 4% Thus, $1 invested at 4% compounded quarterly for 8 yr. amounts to $1.37494; if compounded semi-annually, it will amount to $1.37279. $2500 invested at 4% compounded quarterly for 8 yr. amounts to 2500 $1.37494, or $3437.35. EXERCISE 20 From the table above, what is: 1. a. The compound amount of $1 invested at 4% compounded annually for 5 yr.? b. The compound interest on $1 at 4% compounded annually for 5 yr.? 2. a. The compound amount of $1 invested at 4% compounded semi-annually for 10 yr.? b. The compound interest on $1 invested at 4% compounded semi-annually for 10 yr.? 3. a. The compound amount of $1 invested at 4% compounded quarterly for 7 yr.? b. The compound interest on $1 invested at 4% compounded quarterly for 7 yr.? |