When interest is compounded semiannually, the number of interest-bearing periods is twice the number of years and the interest for each period is one half the given interest. When interest is compounded semiannually, find the amount of 1. $200 for 11 yr. at 4%. (11⁄2 years at 4%, means 3 periods at 2%.) 7. $120 for 2 yr. at 5%. 4. $200 for 2 yr. at 5%. 8. A boy won a prize of $250 for an essay on Thrift and put the money in a savings bank which paid 3% interest semiannually. To how much did this amount in 11⁄2 years? 9. Compare the amount of $1,500 for 2 years at 4% compounded annually with the same principal compounded semiannually. When interest is compounded quarterly, there are 4 interest-bearing periods in each year, the interest for each period being one fourth the rate for the year. The number of periods, then, is 4 times the number of years and the interest for each period is the rate for the year. With interest compounded quarterly, find the amount of 1. $300 for 1 yr. 3 mo. at 4%. (1 yr. 3 mo. is 11 yr. periods, at 1%.) 2. $800 for 1 yr. at 4%. 1 yr. at 4% means 4 × 14, or 5 4. $900 for 1 yr. 3 mo. at 4%. 5. $750 for 9 mo. at 3%. 3. $700 for 1 yr. at 4%. 6. How much more would $150 amount to in one year at 4% compounded quarterly than in one year at 4% simple interest? than in one year at 4% compounded semiannually? INTEREST TABLE This table gives the compound amount of $1.00 for different periods, at different rates. From the above table we can determine very quickly the amount of one dollar for any number of periods through ten, for different rates of interest. Before working the examples on page 101, practice reading from the above table amounts of $1 for different periods and rates. A. Find the amount of $75 for 7 years at 5%, if the interest is compounded annually. This means 7 periods at 5%. In the 5% column and opposite period 7, we find $1.407, the amount of $1.00 for 7 periods at 5% compound interest. 75 X $1.407 $105.53, the amount of $75 at compound interest for 7 years at 5%. = UNIV. OF B. Find the amount of $125 for 2 years at 4%, interest compounded semiannually. 2 years at 4% means 5 periods at 2%. In the 2% column and opposite period 5, we find $1.104, the amount of $1.00 for 5 periods at 2%. 125 X $1.104 = $138, the amount of $125 for 5 periods at 2%, or, 2 years at 4%. From the interest table on page 100, find the amount of the following principals under the given conditions. 12. Find the amount of $1,500, drawing interest 3 yr. at 5% compounded semiannually. 13. Find the amount of $750 for 7 years, with interest at 44% compounded annually. 14. A man left $2,000 in a savings bank for 5 years, drawing compound interest semiannually at 4%. To what did it amount in that time? Postal Savings The United States Government, through its Postal Savings system, offers a safe deposit for savings. The fact that the system is backed by the government makes it appeal strongly to many depositors to whom security is the main consideration. The interest rate is very small, only 2% a year. Amounts of $1.00 or more deposited at any time begin drawing interest from the first of the next month, provided the money is not withdrawn for a year. If $10 is deposited on February 15, it will begin drawing interest on March 1. If the money is not withdrawn until the following March 1, the interest for the year will be paid. If it is withdrawn before March 1, no interest will be paid. Interest, then, is paid only for full years. Money which is deposited and then withdrawn in less than one year draws no interest. Money kept on deposit for 1 year 11 months draws interest for only one year. When a person deposits money in the Postal Savings system, he fills out a card giving his age, birthplace, and such other information as will identify him. He is then given a Postal Savings Certificate for the amount deposited. This certificate is payable only to him and at the post office where he made the deposit. The Postal Savings system appeals especially to newcomers to this country who are attracted by the security it offers as a deposit for their savings. Later, when they learn more about savings banks, they generally deposit their savings where they can get a higher interest rate. What would be the amount of $150 deposited September 19, 1923, and withdrawn July 2, 1924? GENERAL TESTS I 1. Which is greater, 18% of 345 or 23% of 245? How much greater? 2. How much is 46.8 multiplied by 100? 46.8 divided by 10? 46.8 divided by 1,000? 3.景+++音 4. 36.5 X 208.4 5. 9 X 2 wk. 3 da. 6. 250.92 ÷ 6.15 7. Shoes costing a merchant $3.50 a pair were marked for a profit of 30%. If the cost of selling is estimated at 45¢ per pair, how much did the merchant make on each pair? 8. Ten boys bought $18 worth of provisions for a hike, planning to share the cost equally. Two other boys joined the party. How much less did each of the first ten boys have to pay than he expected? II 1. Add $7,695.38 and $4,067.25 and subtract the sum from $50,000. 6. Find the cost of a $37.50 suit that has been marked down 20%. 7. A man who received a salary of $2,200 planned to use not over 12% of his salary for room rent. He secured a room for $4.75 a week. Did this carry out his plan? 8. Which is the greater discount, one of 30%, or a double discount of 20% and 10%? |