4. At what rate per cent. will $5.37, in 4 years and 12 days, give $173272 interest? Ans. 8 per cent.

5. At what rate per cent. will $4070, in 3 months, give $91.575 interest? Ans. 9 per cent.

PROBLEM IV.

Given the principal, the rate per cent., and the interest, to find the time.

If the time for which interest is computed be doubled, other things being the same, the interest will be doubled; if the time is tripled, the interest will be tripled. And in all cases, the interest for any particular time is as many times greater than the interest for one year, as the particular time is greater than 1 year. Hence, we have this

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 $167085; 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 double itself at 7 per cent.? 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 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

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 $1 is of $1.06;

DISCOUNT.

that is, the present value of $1 is of $1, or

247

And

since the present worth of two dollars is twice as great as

for one dollar, we have

And in the same way we find

for the present worth of $2.

for the present worth

of 83; % for the present worth of $10.

Had the time been 6 months instead of one year, then would be the present worth of $1; would be the present worth of $2; would be the present worth

of $10.

If we reckon 7 per cent. interest, the present worth of for one year would be, for 6 months it would be T5; 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 Subtract the present worth from the in the present worth. 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 $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 number of If we subtract the present dollars in the present worth. 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 7 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