Advanced Arithmetic

WRITTEN EXERCISE

1. If a man's salary was decreased 21% and was then $1170 a year, how much was it before the decrease?

2. If a man's salary was increased 5% and was then $1207.50 a year, how much was it before the increase? 3. If you work 312 days in a year, at $1.75 a day, and save $91, what

5. If you worked at a salary of $1.25 a day, and spent 80% of your income for living expenses, and saved $75 in a year, how many days did you work?

6. If you should work 310 days in a year, and spend 82% of your income for living expenses, how much would you have to earn a day in order to save $108.50 a year?

7. A boy is offered a salary of $7.50 a week for the first year in a store, 331% more the second year, and 50% beyond that thereafter. What will be the total salary for 3 years, allowing 52 weeks to the year?

8. If a carpenter earns $3 a day and works 300 days in one year, what will be the alteration in annual income if his daily wages are increased 10% the following year and the working days are decreased 10% in number?

9. A boy who has been working this year at $25 a month is offered either an increase of 20% for next year or a salary of $7 a week. Which will bring the more income, and how much more per year? (Use 52 wk.)

10. A girl who has been working in a factory at $21.67 a month, is offered an increase of 10% where she is or a salary of $5.60 a week elsewhere. Which will bring the more income, and how much more per year? (Use 52 wk.)

11. A boy went to work at 90 a day. The second year his wages were increased 20%, the third year they were 42 a day more than the second, and the fourth they were increased 33%. At 300 working days to the year, what was his total income for each year?

12. A girl entering a trade school finds that graduates from the dress making department receive on an average $4.60 a week the first year; those from the millinery department, 5% less; those from the embroidery department, 5% more than the dressmakers; and those from the operating department, 663 % as much as the last two together. Find the average wages of each, and tell which department the girl probably entered. (Use 52 wk.)

13. A girl leaving the public school finds she can enter a city shop at a salary of $3 a week the first year, with 163% more the second year, and a 142% increase the third year. Instead of this she enters a trade school for a year, tuition free. She then receives a salary of $5 a week the first year and 20% more the second year. Counting 50 working weeks a year, how much more does she receive in three years by the plan she follows after leaving the public school than she would have received without the trade-school training?

BANK ACCOUNTS

110. A bank account essential. One thing essential to any one who hopes to succeed is a bank account. Any one may "open an account," as it is called, as soon as he begins to save even a small amount. In most parts of the country small sums are usually deposited in savings banks.

111. The savings banks. To deposit money a person simply goes to the bank, says that he wishes to open an account, and leaves his money with the officer in charge. The officer gives him a book in which the amount is written, and the depositor writes his name in a book of signatures, for identification. When he wishes to draw out any money, he takes his book to the bank, states how much he wishes, signs a receipt (in some parts of the country he makes out a check), has the amount entered in his book, and the money is paid to him if it does not exceed his deposits, his "balance," as they say. If he forms the habit of depositing money when he has any to spare, and never drawing except in an emergency, he will be surprised to see how it accumulates.

WRITTEN EXERCISE

1. What does 25 ct. saved a day amount to in a year? 2. How much will 15 ct. a day, 310 days a year, amount to in 10 years, not counting interest?

3. If a boy, beginning when he is 16, saves 25 ct. a day for 300 days a year, and deposits it in a savings bank, how much will he have when he is 21, not counting interest?

4. If a father gives his daughter $1 when she is 1 yr. old, $2 on her next birthday, and so on until she is 21, depositing it for her in a savings bank, how much will she have when she is 21, not counting interest?

5. A man saves on an average 25 a day the first year he works on a certain farm, and 120% as much the second year, depositing it in a savings bank. If he works 306 days each year, how much does he save in the two years?

6. A farmer's savings-bank deposits average $25 a month during a certain year, and 97% as much during the next year. The year following he deposited 110% as much as he did the second year. How much did he deposit during the three years?

7. If a man saved $1 a week during the year in which he was 21, and increased his savings each year by 10% on the amount of the preceding year, and worked 50 weeks a year, how much would he save during the year in which he was 29 years old?

8. A merchant saves $375 the first year he is in business. The second year he increases his savings one third. The third year they are only 85% as much as the second year. The fourth year they increase 30%. How much does he save in the four years?

9. A man works on a salary of $15 a week for 50 weeks in a year. His expenses are $15 a month for house rent, 60% as much for clothing, 300% as much for food as for clothing, and 20% as much for other necessary expenses as for food. How much of his salary can he reserve for the savings bank?

10. A clerk in a store had a salary of $12 a week two years ago, and a commission of 2% on the goods sold by him. That year he worked 48 weeks and sold $2350 worth of goods. Last year his salary was increased 25%, his commissions remaining the same. He worked 49 weeks and sold $2750 worth of goods. How much was his income increased?

112. How savings banks pay interest. Savings banks usually pay interest every six months. This is added to the principal, and the amount draws interest.

113. Compound interest. When the interest is added to the principal as it becomes due, and the amount draws interest, the owner is said to receive compound interest. Compound interest is no longer allowed on notes. But if any one collects his interest when due, and at once reinvests it, of course he practically has the advantage of compound interest. The method of finding compound interest is substantially the same as that used in simple interest.

114. Illustrative problem. Required the amount of $2000 invested in a savings bank at 4% annually, the interest compounded semiannually, for 2 years.

The simple interest for the same length of time is $160, $4.87 less than the compound interest.

$2000
.02

= first principal