4. In what time will a given principal double itself at 7 per cent.? Ans. 144 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 4 per cent. ? Ans. 223 years. The following table gives the time required for a given principal to double itself at simple interest at various rates

117. DISCOUNT is an allowance made for the payment of money before it is due.

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

When the interest is at 6 per cent., the amount of $1, for one year, is $106; therefore, the present worth of $106, due one year hence, is $1. If the present worth of $1.06 is $1, it follows that the present value of $1 will be the same fractional part of $1, that 31 is of $1.06;

$1

that is, the present value of $1 is T. of $1, or 8. And since the present worth of two dollars is twice as great as for one dollar, we have for the present worth of $2.

$2

$3

And in the same way we find for the present worth

1.06

of $3; for the present worth of $10.

1.06

Had the time been 6 months instead of one year, then would be the present worth of $1;

the present worth of $2;

of $10.

would be

would be the present worth

If we reckon 7 per cent. interest, the present worth of $1 for one year would be, for 6 months it would be ; and so on for other sums and other rates of interest. 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 whose present worth is required, by this amount, and it will give the number of dollars in the present worth. Subtract the present worth from the given sum, 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 $106, 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, and 6 months hence, at 5 per cent.?

due 3 years

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 number of dollars in 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 71⁄2 months. What is the present worth of the goods, interest being at 7 per cent.? Ans. $1437.126.

Ans. $49.14.

6. What is the present worth of $50, payable at the end of 3 months, at 7 per cent.? 7. What is the discount on $100, due 6 months hence, at 6 per cent.? 8. What is the discount on $750, due 9 months hence, at 7 per cent.? Ans. $37.411.

Ans. $2.913.

9. What is the present worth of $3471-20, due 3 years and 9 months hence, at 41 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. 13. Bought a bill of goods for $1200, one third payable in 3 months, one third in 6 months, and the remaining one third in 9 months. How much ready cash ought to pay for the goods, if we consider money with 6 per cent.? Ans. $1165-21+.

COMPOUND INTEREST.

118. WHEN, at the end of a year, or of any given time, the interest due is added to the principal, and the amount thus obtained is considered as a new principal, upon which interest is to be cast for another given period, to be added in like manner to form a second new principal, and so on, the last amount thus obtained is called the AMOUNT AT COMPOUND INTEREST. If from this amount we subtract the original principal, we obtain the coм

POUND INTEREST.

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

EXAMPLES.

1. What is the compound interest of $1000, for 3 at 7 per cent.?

years

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

3. What is the compound interest of $630, for 4 years, at 5 per cent.?

Ans. $135.769. 4. What is the amount at compound interest, of $50, for 3 years, at 5 per cent.? Ans. $57.881. 5. What is the compound interest of $1000, for 4 years, at 6 per cent. ?

Ans. $262.477.

BANKING.

119. A BANK is an incorporated institution, created for the purpose of loaning money, receiving deposits, 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 denomi