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In the Bank.
INTEREST ON DAILY BALANCES.
Sometimes a person who has a large but constantly varying sum of money which he wishes to keep on deposit in some reliable bank, can arrange with the bank officials to receive at the end of each month 2% or more on his daily balances. The accountant at the bank ordinarily employs carefully prepared tables for computing the interest due a depositor. Regarding 360 days as a year, accounts like the following can easily be computed without the aid of interest
The interest on $1.00 for 160745 days at 6% is (160745+6) 26790 mills; at 2% it is one third this number (26790÷3) or 8930 mills. This equals $8.93.
1. Make an enlarged copy of the above account and extend the balances and interest for the month of May. Compute the interest at the rate of 2% per annum.
* Mr. Smith is entitled to interest on $5000 from Apr. 1 to Apr. 5, 4 days. (5000×4 =20000). This equals the interest on one dollar for 20000 days. Hence "20000" is carried into the interest column.
+ In computing interest on daily balances, it is customary to omit any fraction of a dollar that may appear in the principal. In some banks interest is computed on full hundreds of dollars only; thus, if the balance is $5742 interest is allowed on $5700.
3) 26790 mills.
Interest on Daily Balances.
Rule paper as suggested on the preceding page, arrange in proper form the accounts given below, and find the balance of each account on the last day of the month, allowing interest on daily balances at the rate of 2% per annum.*
June 1, deposited $8000. June 6, deposited $400.
June 18, withdrew $248.50. June 20, withdrew $675.20.
May 6, deposited $4270. May 7, withdrew $342.50.
Aug. 10, deposited $10000.
Aug. 15, deposited $5000.
* These problems are mainly for a test of the ability of the student to work in figures with care and to secure accurate results. Let no pupil be satisfied with his self-training in this respect unless he can do all the work suggested on this page, and present it to his teacher in good form and absolutely free from errors in figures. Unless he can do this, he would, with his present attainments, be of little value as an accountant. The business world demands accuracy in accounts.
It is sometimes necessary in business to find the compound amount of money at interest. This is done by adding the interest to the principal at the end of a specified period and using the sum thus found as a new principal upon which the interest is computed and the amount obtained as before. This process is repeated as many times as there are interest bearing periods. To find the compound interest, subtract the original principal from the compound amount.
1. What is the compound amount of $200 for 2 years, interest at 6% per annum to be compounded annually?
2. What is the compound interest of $200 for 2 years, at 6% per annum to be compounded annually?
3. How much more is the compound interest of $200 for 2 years at 6%, than the simple interest of the same sum for the same time and rate? Why?
4. Without solving the two interest problems in full, tell how much more the compound amount of $500 for 2 years at 6%, is, than the simple amount of the same sum for the same time and rate.
5. Find the compound amount of $350 for 2 yr. 6 mo. at 6% per annum, interest to be compounded annually.*
6. Find the compound amount of $350 for 2 yr. 6 mo. at 6% per annum, interest to be compounded semi-annually.† Compare the answer to this problem with the answer to Problem 5.
7. Find the compound amount of 425.40 for 2 yr. 4 mo. 12 da. at 6%, interest to be compounded annually.
8. If Mark Mahan puts $100 at interest at the rate of 6% per annum, on the first day of each January for 8 successive years, and if at the end of each year he collects and loans the interest due him, at the same rate, all this will amount to how much, 8 years from the time of his first investment?
* Interest must be computed for three periods-the first two, one year each, and the third, six months.
+ This calls for the compound amount for five periods at 3%.
Showing the compound amount of $1.00 at 2, 3, 4, 5, and 6 per cent, for any number of periods, from 1 to 20.
1. Solve again the problems on page 295, using in the work, items from the above table.*
NOTE.-In Savings Banks the interest due depositors is compounded usually semi-annually; that is, the interest if not with. drawn, is added to the principal every 6 mo.
2. Twelve hundred dollars deposited in a savings bank that pays interest at the rate of 4% per annum and compounds it every 6 mo., will amount to how much in 10 years? †
*To solve problem 8 on page 295, it will only be necessary to add the first eight numbers in the "6 per cent" column and multiply the sum by 100. Why?
+ Think of this money as loaned for 20 "2 per cent" periods.
It is often important to know the exact present value of a promise to pay a sum of money after a specified number of years, months, or days. The rule for solving such problems is,—Divide the amount to be paid by the amount of $1.00 for the given time and at the current rate. Discuss the reasonableness and accuracy of this rule in its application to the special cases presented on this page.
1. What is the present value of a good note for $477, drawing no interest, and due one year hence, the current rate being 6%?
2. Prove your answer to Problem 1 to be correct by finding the amount of it for one year at 6 per cent.
3. What is the present worth of $500 due 2 years hence, the current rate for money being 6% interest payable annually?*
4. If a father should give to one son a note for $500 payable in 2 years without interest, and to another son, an amount of cash equal to your answer to Problem 3, and the second son should loan his money for two years at 6% with interest payable annually, and at the end of the first year should collect the interest due and loan it for one year at 6%, how would the amounts received by the two sons compare at the end of two years?
5. What is the present worth of a good note for $600, that matures 2 years hence and draws interest from the present time at 8%, the interest being payable annually, and the current rate for money being 6%, interest payable annually?†
6. What is the present value of a good note for $800, that matures 3 years hence, and draws interest from the present time at the rate of 4% per annum payable annually, the current rate for money being 6% interest payable annually?
*Since money is worth 6% interest payable annually, one dollar in two years would amount, not to $1.12, but to $1.1236. See table on preceding page.
+ Observe that this problem calls for the present value of $48 due 1 year hence, and $648 due 2 years hence.