1 LXX. THE PRINCIPAL, RATE PER CENT., AND INTEREST BEING GIVEN, TO FIND THE 1

TIME.

1. William received $18 for the interest of $200 at 6 per cent.; how long must it have been at interest?

The interest on $200 for 1 yr. at 6 per cent. is $12; hence $18-12-1 =1 years, the required time, Ans.

Q. What, then, is the RULE ?

A. Divide the given interest by the interest of the principal for 1 year at the given rate; the quotient will be the time required, in years and decimal parts of a year.

2. Paid $36 interest on a note of $600, the rate being 6 per cent; what was the time? A. 1 year.

3 Paid $200 interest on a note of $1000; what was the time, the rate being 5 per cent.? A. 4 years.

4. On a note of $60, there was paid $9,18 interest, at 6 per cent.; how long was the note on interest?

A, 2,55 yrs 2 yrs. 6 mo. 18 da.

COMPOUND INTEREST.

¶ LXXI. 1. Rufus borrows of Thomas $500, which he agrees to pay again at the end of 1 year, together with the interest, at 6 per cent.; but, being prevented, he wishes to keep the $500 another year, and pay interest the same as before. How much interest ought he to pay Thomas at the end of the two years?

In this example, if Rufus had paid Thomas at the end of the first year, the interest would have been $500 x 6=$30, which, added to the principal, $500, thus, 500+30,530, the sum or amount justly due Thomas at the end of the first year; but, as it was not paid then, it is evident, that, for the next year, (2d year,) Thomas ought to receive interest on $530, (being the amount of the first year.) The interest of $530 for 1 year is 530 X 6=$31,80, which, added to $530,561,80, the amount for 2 years; hence, $561,80-$500=$61,80, Compound Interest, the Answer.

This mode of computing interest, although strictly just, is not authorized by law.

Q. When the interest is added to the principa, at the end of 1 year, and on this amount the interest calculated for another year, and so on, what is it called?

A. Compound Interest.

Q. How, then, may it be defined?

A. It is interest on both principal and interest. Q. What is Simple Interest?

A. It is the interest on the principal only.

Hence we derive the following

Q. How do you proceed?

RULE.

A. Find the amount of the principal for the 1st year, by multiplying as in Simple Interest; then of this amount for the 2d, and so on.

Q. How many times do you multiply and add?

A. As many times as there are years: the last result will be the amount.

Q. How is the compound interest found?

A. By subtracting the given sum, or first principal, from the last amount.

More Exercises for the Slate.

2. What is the compound interest of $156 for 3 yrs. $156 given sum, or first principal.

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3. What will be the amount of $500 for 4 years, at compound interest? A. $631,238+.

4. What is the amount of $500 for 4 years, at simple interest? A. $620.

5. What will be the amount of $700 for 5 years, compound interest? A. $936,7571% +.

6. What will be the amount of $700 for 5 years, at simple interest? A. $910.

7. What will be the amount of $1000 for 3 years, at com. pound interest?-1191016. $1500 for 6 years?-21277786. $2000 for 2 years?-224720. $400 for 7 years?-601452.

A. $6167,446+t. 8. What is the compound interest of $150 for 2 years?-1854. $1600 for 4 years?-4199631. $1000 for 3 years?-191016. $5680 for 4 years?-1490869. $500 for 3 years?-95508. A. $2215,896++.

9. What is the compound interest of $600,50 for 2 years, at 2 per cent.?-242602. At 3 per cent.?-365704. At 4 per cent. ?490008. At 5 per cent. ?-615512. At 7 per cent. ?-870124. At 10 per cent. ?-126105. A. $384,50.

10. What is the difference between the simple interest of $200 for 3 years, and the compound interest for the same time? A.$2,203.

11. What is the compound interest of $600 for 2 years 6 months?

In calculating the compound interest for months and days, first find the amount for the years, and on that amount calculate the interest for the months and days; this interest, added to the amount for the years, will be the interest required.

A. $94,38,4+. 12. What is the compound interest of $500 for 3 yrs. 4 mo. A. $107,418+. 13. What is the difference between the simple and compound interest of $200 for 3 yrs. ?-22032. For 4 yrs. 6 mo. ?-60702. For 2 yrs. 8 mo. 15 da.?-17706. A. $10,044.

As the amount of $2 is twice as much as $1, $4, 4 times as much, &c., hence, we may make a table containing the amount of the 1£, or $1, for several years, by which the amount of any sum may be easily found for the same time.

TABLE,

Showing the amount of 1£, or $1, for 20 years, at 5 and 6 per cent., at compound interest.

6

4

2,26090

5

6

1,21550 1,26247 14 1,97993

1,27628 1,33822 15 2,07892 2,39655 1,34009 1,41851 16 2,18287 2,54035 7 1,40710 1,50363 17 2,29201 2,69277 8 1,47745 1,59384 18 2,40661 2,85433 9 1,55132 1,68947 19 2,52695 3,02559 10 1,62889 1,79084 20 2,65329

3,20713

14. What is the compound interest of $20,15 for 4 years, at per

cent. ?

By the Table, $1 at 6 per cent. for 4 years, is $1,26247, X $20,15=$25,438, amount, from which $20,15 being subtracted, leaves $5,28870 +.

15. What is the amount of $10,50, at 5 per cent. for 2 years?115762. For 6 years?-140709. For 8 years?-155132. For 15 years?-218286. For 17 years?-240661. For 20 years?-278595. $114,914+, Ans.

Any sum, at simple interest, will double itself in 16 years 8 months; but at compound, in a little more than half that time, that is, in 11 years, 8 months and 22 days. Hence, we see that there is considerable difference in a few years, and when compound interest is permitted to accumulate for ages, it amounts to a sum almost incredible. If 1 cent had been put at compound interest at the commencement of the Christian era, it would have amounted, at the end of the year 1827, to a sum greater than could be contained in six millions of globes, each equal to our earth in magnitude, and all of solid gold, while the simple interest for the same time would have amounted to only about one dollar. The following question is inserted, more for the sake of exemplifying the preceding statement, than for the purpose of its solution. The amount, however, at compound interest, may be found, without much per plexity, hy ascertaining the amount of 1 cent for 20 years, found by the Table, then making this amount the principal for 20 years more, and so on for the whole number of years.

16. Suppose 1 cent had been put at interest at the commencement of the Christian era, what would it have amounted to at simple, and what at com pound interest, at the end of the year 1827? A. Simple, $1,106; com pound, $172616474047552529470760914974711959976620354-5 nearly.

EQUATION OF PAYMENTS.

¶ LXXII. Q. What is the meaning of equation?
A. The art of making equal.

Q. What is equation of payments?

A. It is the method of finding an equal or mean time for the payment of debts due at different times.

1. In how many months will $1 gain as much as $2 will gain in 6 months? A. 6 × 2 = 12 months.

2. How long will it take $1 to gain as much as $5 will gain in 12 months? A. 60 months.

3. How many months will it take $1 to be worth as much as the use of $10, 20 months? A. 200 months.

4. A merchant owes 2 notes, payable as follows: one of $8, to be paid in 4 months; the other of $6, to be paid in 10 months but he wishes to pay both at once: in what time ought he to pay them?

4 x 832, therefore, $8 for 4 mo. = 10 × 6= 60; therefore. $5 for 10 mo. ==

14

for 32 mo., and $1 for 60 me.

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