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35. Find the amount of $356.25 in 4 yrs., at 5% compound

interest.

36. Find the amount of $637.50 in 2 yrs. 6 mos., at 4% compound interest.

37. Find the compound interest of $800 in 3 yrs. 9 mos., at 6%.

38. Find the compound interest of $39.35 in 1 yr. 9 mos., at 5%.

If the interest be payable semi-annually, quarterly, etc., the half, quarter, etc., of the rate per cent must be used, and the amount obtained for each half-year, quarter-year, etc.

39. Find the compound interest of $300 in 2 yrs., at 4%, interest being payable semi-annually.

40. Find the compound interest of $525 in 1 yr. 6 mos., at 5%, interest being payable quarterly.

41. Find the compound interest of $10,000 in 6 mos., at 6%, interest being paid monthly.

Ex. What principal will in 3 yrs. produce $780.40 compound interest, at 4%?

The amount of $1 for 1 yr. at 4% is $1 x 1.04;

for 2 yrs. is $1 × 1.04 × 1.04 $1× 1.042;
for 3 yrs. is $1 × 1.042 × 1.04 = $1×1.043.

Hence, the amount of $1 for 3 yrs. at 4% is $1.124864.
The interest is $1.124864-$1 = $.124864.

$780.40.124864 = $6250.

42. What principal will amount to $137.81 in 2 yrs., at 5% compound interest?

43. What principal will amount to $1860.96 in 3 yrs., at 6% compound interest?

44. What principal will amount to $1500 in 1 yr., at 4% compound interest, payable quarterly?

45. What principal will produce $100 in 1 yr. 6 mos., at 6% compound interest, payable semi-annually?

ANNUAL INTEREST.

369. Annual interest is simple interest on the principal and on each year's interest from the time each interest is due until settlement.

Ex. Find the interest due July 4, 1881, on a note dated May 4, 1877, for $850, with interest payable annually, at 7%.

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$275.69 total interest due.

The simple interest on the principal is $247.92.

The first year's interest, $59.50, remains overdue 3 yrs. 2 mos. ; the second year's, 2 yrs. 2 mos.; the third year's, 1 yr. 2 mos.; the fourth year's, 2 mos. The interest on $59.50 for the sum of these periods, 6 yrs. 8 mos., is $27.77. Hence, the total interest due is $247.92 + $27.77 $275.69.

46. Find the interest due May 19, 1881, on a note dated Dec. 26, 1877, for $1224.60, with interest payable annually, at 5%, when no interest has been paid. 47. Find the amount due May 27, 1881, on a note dated Jan. 4, 1879, for $215.50, with interest payable annually at 51%, when no interest has been paid.

48. Find the amount due Jan. 16, 1881, on a note dated Jan. 8, 1879, for $3115.20, with interest payable annually at 5%, when no interest has been paid.

49. Find the amount due Jan. 18, 1881, on a note dated Jan. 8, 1877, for $2875, at 6% (1) simple interest; (2) annual interest; (3) compound interest.

NOTE. When partial payments have been made on a note, the annual interest, by the law of Vermont, is found to the end of the first year in which any payments have been made, and the sum of the payments, with the interest reckoned on each to the end of that year, is applied to cancel any interest that may have accrued on the yearly interest, then to cancel the yearly interest, and then to the payment of the principal.

The law of New Hampshire is the same as that of Vermont; but if at the time of any payment no interest is due, except what is accruing for the year, and the payment is less than the interest due at the end of the year, then no interest is allowed on the payment.

The Connecticut Rule is similar to the United States Rule; but when less than a year's interest has accrued at the time of a payment, except it be the last payment, the difference between the amount of the principal for an entire year and the amount of the payments made that year is taken as the new principal. But if the interest which has accrued at the time of a payment exceeds the payment, no interest is computed on the payment.

These are special rules for the guidance of the State Courts or their agents, whenever it becomes necessary for them to determine the amount due on a note. But it is the general practice among business men to settle notes "with interest" that run for a year or less, by the Merchants' Rule; that run for more than a year, by the United States Rule; and to settle notes "with interest annually," or "semi-annually,” if the interest be not paid when due, by compounding the interest with the principal.

The Legislature of each State has fixed the legal rate of interest for that State. Practically, however, the rate of interest is determined by the law of supply and demand. When the supply is greater than the demand, the rate of interest is low; when the supply is less than the demand, the rate of interest is high.

CHAPTER XVIII.

STOCKS.

370. The name stock is applied to the capital of banks, railroads, and other incorporated companies.

The capital of a company is usually divided into shares, of which the original value is $100, or some other fixed sum; but the market value at any time is estimated by the current price per share.

371. When the market value of stock is equal to its original value, it is said to be at par. In quotations of stocks par is generally represented by 100; and when stock is quoted at above 100, it is said to be at a premium; below 100, at a discount. The premium or discount is the difference between the quotation and 100.

Thus, when the price of a stock on a given day is 91, or, as it is commonly expressed, when the stock is at 91, the meaning is, that $100 stock costs on that day $91 money. Or that if 100 be the representative of any quantity of stock, 91 will represent the corresponding value in money. In this case the stock is said to be 9% discount.

The buying and selling of stocks is conducted through the agency of stock-brokers, who receive a brokerage on the stock. The brokerage is generally reckoned at of 1% on the par value of the stock. Thus, if a broker sells stock for a person at 91, that person receives 907; and if he buys stock for a person at 91, that person pays 911.

(1) How much would be received for 52 shares of stock, $100 each, at 89?

will represent the brokerage. 89-89%, price to the seller.

Hence, 1 share will bring $89; and 52 shares, 52×$89%

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(2) What amount of stock at 84 may be bought for

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$9393.375?

If be the brokerage,

84+84, price to the buyer.

Hence, $.84 buys $1 stock, and $9393.375 will buy

$9393.375÷.84§=$11,100. Ans.

(3) What is the quoted price of stock when $42,464.25 is paid for $46,600 stock?

If $46,600 stock cost $42,464.25,

then $1 stock costs $42,464.25÷ 46,600 = $.914.

Hence, the stock is quoted at 91 - brokerage = 91. Ans.

EXERCISE LXXIII.

In the following examples the prices of stocks include brokerage unless otherwise stated:

1. Find the cost of $4000 stock, at 109.
2. Find the cost of $2500 stock, at 98.
3. Find the cost of $3900 stock, at 78.

4. Find the cost of $4700 stock, at 1001.

5. Find the cost of $1250 stock, at 87, brokerage .

6. How much bank stock, at 751, may be bought for

$8729?

7. How much railroad stock, at 91, may be bought for

$4237?

8. How much railroad stock may be bought for $6305, at

1211?

9. How much railroad stock may be bought for $5137.50,

at 1024 ?

10. How many $100 railroad shares, at 681, may be bought

for $1650?

11. What must be the price of stock, in order that $9200 stock may be bought for $8970?

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