ANNUAL INTEREST 525. In some states when a written agreement contains the expression "with interest payable annually," simple interest may be collected upon the principal and upon each year's interest that has not been paid when due. This is called annual interest. WRITTEN EXERCISES 526. 1. No interest having been paid, find the amount due in 3 years 6 months 6 days on $1000, with interest payable annually at 6%. Principal SOLUTION Simple interest on $1000 at 6% for 3 yr. 6 mo. 6 da. $10001 211 The amount equals the principal, plus the simple interest for the entire time, plus the interest on each year's interest for the time it remains unpaid. Find the amount, with annual interest, of: 2. $6200 for 2 yr. 6 mo. at 6% 3. $5850 for 4 yr. 3 mo. at 4% 4. $8760 for 3 yr. 8 mo. at 5% 5. $10,000 for 2 yr. 4 mo. 24 da. at 3% 6. $24,000 for 3 yr. 3 mo. 12 da. at 5% 7. $36,500 for 1 yr. 7 mo. 18 da. at 6% COMPOUND INTEREST 527. Interest on the principal and its unpaid interest, combined at regular intervals, is called compound interest. Interest may be compounded with the principal annually, or semiannually, or quarterly, etc. Compound interest cannot usually be enforced by law, even though it is specified in the contract. Nevertheless the subject is of importance since it is at the basis of computations concerning investments, for there is nothing to hinder a inan from drawing his interest and investing it. WRITTEN EXERCISES 528. 1. Find the amount of $400 for 2 yr. 4 mo. at 6%, interest compounded annually; also find the compound interest. Since the amount of $400 at compound interest is $458.43, the compound interest is $458.43 $400, or $58.43. NOTE. - Unless otherwise specified, interest is understood to be compounded annually. If compounded semiannually, the rate must be considered one half the annual rate mentioned; if quarterly, one fourth, etc. When the time consists of years, months, and days, the amount is to be found for the greatest number of entire periods, as years, half years, quarter years, etc., and the simple interest upon this for the rest of the time. Find the amount and the compound interest of: 2. $400 for 2 yr. at 5% 3. $1000 for 3 yr. at 4 % 4. $1500 for 4 yr. 6 mo. at 6 % 5. $5000 for 2 yr. at 6 %, payable semiannually 6. $5000 for 2 yr. at 6 %, payable quarterly 7. $8000 for 1 yr. 8 mo. at 4 %, payable quarterly 8. Find the amount of $1000 for 10 years at 4 % compound interest; at 4 %, compounded semiannually. SOLUTIONS 1. By the table on the next page the amount of $1 at 4% compound interest for 10 years is $1.480244. Hence the amount of $1000 for the same time at the same rate is 1000 × $1.480244, or $1480.24. 2. If the rate is 4% compounded semiannually, there are 20 interest periods and the rate for each is 2%. Therefore the amount of $1000 for 10 years at 4%, compounded semiannually, is the same as the amount of $1000 for 20 years at 2%, compounded annually. By use of the table this amount is found to be $1485.95. Find, by the table, the amount at compound interest of: 9. $1000 for 10 yr. at 5 % 10. $5000 for 20 yr. at 31 % 16. $86.48 for 18 yr. 10 mo. 15 da. at 6 % 17. $75.50 for 15 yr. 6 mo. 3 da. at 4 % 18. $5000 for 8 yr. at 6 %, payable semiannually 19. $6500 for 4 yr. 4 mo. 10 da. at 4 %, payable quarterly COMPOUND INTEREST TABLE Amount of $1, at various rates, compound interest, 1 to 20 years 12345678 1.035000 1.040000 1.045000 1.050000 1.060000 1.070000 1.191016 1.225043 1.215506 1.262477 1.310796 1.276282 1.338226 1.402552 1.340096 1.418519 1.500730 529. Reduce: PART IV PRELIMINARY REVIEW 1. 3 bu. 2 pk. 6 qt. to pints. 2. 4 T. 8 cwt. 9 oz. to ounces. 3. 1 mi. 27 rd. 4 yd. 2 ft. 6 in. to inches. 4. 5 A. 100 sq. rd. 18 sq. yd. 3 sq. ft. 36 sq. in. to sq. in. Reduce to higher denominations: day. 5. 73,286". 6. 208,738 sec. 7. 36,894 cu. in. 8. 48,682 gr. (troy). 9. A drill for sowing wheat covered 24 acres of ground per How long did it take to sow a field 216 rd. by 160 rd.? 10. Find the weight of a box of dynamite whose contents measure 4 ft. by 21 ft. by 3 ft., if 1 cubic foot weighs 103 lb. 11. If 420 tons of drinking water are consumed on a vessel during an Atlantic voyage, how many gallons are used? 12. Find the capacity in bushels of a Duluth grain elevator having 2,250,000 cubic feet of storage space. (1 bu.=14 cu. ft.) 13. A body floating in water displaces its own weight of The steamship Baltic weighs 40,000 tons. How many cubic feet of salt water, specific gravity 1.03, does she displace? water. 14. A diamond carat is 3.168 grains. The weight of the largest diamond in the world is 3025 carats. How much more than 1 pounds avoirdupois does the diamond weigh? 15. The English mint is compelled to coin any gold offered it, returning 778. 101d. per ounce 11 fine. Show that the standard weight of a sovereign is 123.27447 grains. |