RULE..

Divide the given interest by the interest of the given principal, for 1 year, at the given rate per cent.

EXAMPLES.

1. In what time will $37.13, at 4 per cent., give $0.7518825 interest?

In this example, we find the interest of $37.13, for 1 year, at 4 per cent., to be $1.67085; therefore, dividing $0.7518825 by $1.67085, we get 0.45 years; this reduced to months and days, gives 5 months and 12 days.

2. In what time will $700, at 7 per cent., give $85.75 interest? Ans. 1 year 9 months. 3. In what time will $100, at 6 per cent., give $100 interest ? That is, in what time will a given principal double itself at 6 per cent. interest? Ans. 16 years.

4. In what time will a given principal

per cent. ?

double itself at 7 Ans. 14 years.

5. In what time will a given principal double itself at 8 per cent.? Ans. 12 years. 6. In what time will a given principal double itself at 5 per cent. ? Ans. 20 years. 7. In what time will a given principal double itself at 41⁄2 per cent.? Ans. 223 years.

The following table gives the time required for a given principal to double itself at simple interest.

DISCOUNT.

of

105. DISCOUNT is an allowance made for the payment before it is due.

money

The present worth of a debt, payable at some future time, without interest, is such a sum of money as will, in the given time, amount to the debt.

When the interest is at 6 per cent., the amount of $1, for one year, is $1.06; therefore, the present worth of $1.06, due one year hence, is $1. We may also infer that the present worth of any sum for one year, will be as many dollars as $1.06 is contained in the given sum. Hence, we have the following

RULE.

Find the amount of $1, for the given time, at the given rate per cent., then divide the sum by this amount, and it will give the present worth. Subtract the present worth from the amount, and it will give the discount.

What is Discount? What is the present worth of a sum of money due at some future period? What is the present worth of $1.06, due one year hence, at 6 per cent. interest? Repeat the Rule for computing discount.

EXAMPLES.

1. What is the present worth of $622.75, due 3 years and 6 months hence, at 5 per cent. ?

In this example, we find the amount of $1, for 3 years and 6 months, at 5 per cent., to be $1.175: therefore, dividing $622.75 by $1.175, we get $530, for the present worth. If we subtract the present worth from the sum, we get $92.75 for the discount.

2. What is the present worth of $4161.575, due 3 months hence, at 9 per cent.? Ans, $4070.

3. What is the present worth of $7.10272, due 4 years and 12 days hence, at 8 per cent.? Ans. $5.37.

4. Sold goods for $1500, to be paid one half in 6 months, and the other half in 9 months. What is the present worth of the goods, interest being at 7 per cent.? Ans. $1437.227.

5. Sold goods for $1500, to be paid at the end of 71 months. What is the present worth of the goods, interest being at 7 per cent.? Ans. $1437.126. NOTE. We see that in this case I do not receive quite as much for my goods as I did in the case of example 4, provided I consider the present worth.*

6. What is the present worth of $50, payable at the end of 3 months, at 7 per cent. ? Ans. $49.14. 7. What is the discount on $100, due 6 months hence, at 6 per cent.? Ans. $2.913. 8. What is the discount on $750, due 9 months hence, at 7 per cent.? Ans. $37.411. 9. What is the present worth of $3471.20, due 3 years and 9 months hence, at 4 per cent. ? Ans. $2970.011. 10. What is the discount of $150, due 3 months and 18 days hence, at 6 per cent. ? Ans. $2.652. 11. What is the discount of $961.13, due 1 year and 5 months hence, at 7 per cent.? Ans. $86.713. 12. What is the discount of $37.40, due at the end of 7 months, at 6 per cent.? Ans. $1.265.

COMPOUND INTEREST.

106. When at the end of each year, the interest due is added to the principal, and the amount thus obtained is considered as a new principal, upon which the interest is cast for another year, and added to it to form a new principal for the next year, and so on to the last year, the last amount thus obtained, is called the AMOUNT AT COMPOUND INTEREST. If from this amount we subtract the original principal, we obtain the COMPOUND INTEREST.

How is the amount of compound interest found? How is the compound interest obtained?

• For still further developments of this curicus subject, see Higher Arithmetic, ART. 67.

EXAMPLES.

1. What is the compound interest of $1000, for 3 years

at 7 per cent.? Principal,

Interest on $1000 for one year,

$1000

70

Ans. $225.043

The compound interest required,

2. What is the compound interest of $100, for 4 years,

at 6 per cent. ?

Principal,

Interest for first year,

$100

6

3. What is the amount of $100, at 6 per cent. per an num, compound interest, for 2 years, when the interest is added in at the end of every six months?

Principal,

Interest on $100 for 6 months, at 6 per cent.,

$100

3

103

4. What is the compound interest of at 5 per cent.?

5. What is the compound interest of at 5 per cent.?

$630, for 4 years, Ans. $135.769. $50, for 3 years, Ans. $7.881.

6. What is the compound interest of $1000, for 4 years, at 6 per cent.?

Ans. $262.477.

3.278181

$112.550881

BANKING.

107. A BANK is an incorporated institution, created for the purpose of loaning money, receiving deposites, and dealing in exchange.

The stock, or amount of money in trade, is limited by law, and owned by various individuals, who are called stockholders.

Banks are allowed to make notes, which are denominated bank bills, which circulate as money, because they are obliged to redeem them with specie.

It is customary for banks, in most cases, when they