COMPOUND INTEREST.

584. Compound Interest is interest not only on the principal, but on the interest added to the principal when it becomes due.

585. 1. What is the comp. int. of $500 in 2 yr. at 6%?

ANALYSIS. -The simple interest of $500 for 2 yr. is $60; the interest of the first year's interest, $30, for the second year is $1.80, which, added to $60, gives $61.80, the compound interest. Or,

The interest of $500 for 1 yr. at 6% is $30, and the amount is $530, which is the principal for the second year; the interest of $530 for 1 yr. at 6% is $31.80, which added to $530 gives $561.80, the final amount; and deducting $500, the original principal, gives $61.80, the compound interest.

What is the compound interest

2. Of $600 for 2 yr. at 5%? | 4. Of $300 for 2 yr. at 10%? 3. Of $100 for 2 yr. at 7%? 5. Of $1000 for 2 yr. at 5% ? What is the amount at compound interest,

6. Of $800 for 2 yr. at 5%? | 8. Of $400 for 2 yr. at 4%? 7. Of $2000 for 2 yr. at 10%? 9. Of $500 for 2 yr. at 8%?

586. 1. What is the comp. int. of $750 for 2 yr. at 6%?

OPERATION.

$750 Prin. for 1st yr. 1.06

$795 Prin. for 2d yr. 1.06

$842.70 Total amount. 750.

$92.70 Compound int.

ANALYSIS.-Since the amount is 1.06 of the principal, the amount at the end of the first year is $795, which is the principal for the 2d year, and the amount at the end of the 2d year is $842.70. Hence, by subtracting the given principal, $750, the result is the compound interest, $92.70.

2. What will $350 amt. to in 3 yr. at 7%, comp. int.? 3. What is the compound int. of $1200 for 3 yr. at 5%!

RULE.-I. Find the amount of the given principal for the first period of time at the end of which interest is due, and make it the principal for the second period.

II. Find the amount of this principal for the next period; and so continue till the end of the given time.

III. Subtract the given principal from the last amount, and the remainder will be the compound interest.

When the time contains months and days, less than a single period, find the amount up to the end of the last period, and compute the simple interest upon that amount for the remaining months and days, which add to find the total amount.

4. What will $864.50 amount to in 4 yr. at 8%, compound interest ?

5. What is the compound interest of $680 for 2 yr. at 7%, interest being payable semi-annually?

6. What is the compound interest of $460 for 1 yr. 5 mo. 18 da. at 6%, interest payable quarterly?

7. What will be the amount of $1250 in 3 yr. 7 mo. 18 da. at 5%, interest being semi-annual?

8. Find the compound interest of $790 for 9 mo. 27 da. at 8%, payable quarterly.

The computation of compound interest may be abridged by using the following table.

To use the table, multiply the given principal by the number in the table corresponding to the given number of years and the given rate. If the interest is not annual, reduce the time to periods, and the rate proportionally. Thus, 2 yr. 6 mo., by semi-annual payments, at 7%, is the same as 5 yr. at 31%; and 1 yr. 9 mo., quarterly payments, at 8%, the same as 7 yr. at 2%.

587. TABLE showing the amt. of $1, at 21, 3, 31, 4, 5, 6, 7, 8, 9, 10, 11, and 12%, compound int., from 1 to 20 years.

Yrs. 2 per cent. 3 per cent. 3 per cent. 4 per cent.

1.025000

1.081600

1.030000 1.035000 1.040000
1.050625 1.060900 1.071225
1.076891 1.092727 1.108718
1.103813 1.125509 1.147523 1.169859
1.131408 1.159274 1.187686 1.216653

1.215506

1.276282 1.338226

1.159693 1.194052 1.229255 1.265319 1.340096 1.418519 1.188686 1.229874 1.272279 1.315932 1.407100 1.503630

8 1.218403 1.266770 1.316809 1.368569 1.477455 1.593848 1.248863 1.304773 1.362897 1.423312 1.551328 1.689479 10 1.280085 1.343916 1.410599 1.480244 1.628895 1.790848 11 1.312087 1.384234 1.459970 1.539454 1.710339 1.898299 12 1.344889 1.425761 1.511069 1.601032 1795856 1.378511 1.468534 1.563956 1.665074 1.885649

2.012197

2.132928

14 1.412974 1.512590 1.618695 1.731676

1.448298 1.557967 1.675349 1.800944 16 1.484506 1.604706 1.733986 1.872981 17 1.521618 1.652848 1.794676 1.947901

20 1.638616

1.598650 1.753506 1.922501
1.806111

1.989789

1.070000 1.080000 1.090000
1.110000 1.120000
1.144900 1.166400 1.188100 1.210000 1.232100

1.100000

1.254400

1.225043 1.259712 1.295029 1.331000 1.367631 1.310796 1.360489 1.411582 1.464100 1.518070 1.402552 1.469328 1.538624 1.610510 1.685058 6 1.500730 1.586874 1.677100 1.771561 1.870414

1.404908

1.573519

1.762342

1.973822

77 1.605781 1.713824 1.828039 8 1.718186 1.850930 1.992563 9 1.838459 1.999005 2.171893 2.357948 2.558036 2.773078 10 1.967151 2.158925 2.367364 2.593742 2.839420

2.578534 2.937194 3.341727 3.797498 15 2.759031 3.172169 3.642482 4.177248 4.784588

4.310440

4887111

5.473565

16 2.952164 3.425943 3.970306 4.594973 5.310893 17 3.158815 3.700018 4.327633 5.054470 5.895091 18 3.379932 3.996019 4.717120 5.559917 6.543551 7.689964 19 3.616527 4.315701 5.141661 6.115909 7.263342 8.612760 20 3.869684 4.660957 5.604411 6727500 8.062309 9.646291

6.130392 6.866040

9. Find by the table the compound interest of $950 for 1 yr. 5 mo. 24 da., at 10%, interest payable quarterly.

OPERATION.

1 yr. 5 mo. 24 da. 5 quarters of a year +2 mo. 24 da.
10% per annum = 21% per quarter.

Amount for 5 yr. at 21%

$950 × 1.131408 $1074.837, amount for 1 yr. 3 mo.
Interest of $1074.837 for 2 mo. 24 da. at 10% = $25.079.
$1074.837+$25.079 = $1099.916, total amount.

$1099.916 — $950 = $149.916, compound interest.

10. Find the amount, at compound interest, of $749.25 for 10 yr. 4 mo., at 7%, interest payable semi-annually. 11. What sum placed at simple interest for 3 yr. 10 mo. 18 da., at 7%, will amount to the same as $1500 placed at compound interest for the same time, and at the same rate, payable semi-annually?

12. At 8%, interest compounded quarterly, how much will $850 amount to in 1 yr. 10 mo. 20 da.?

int.?

13. What will $500 amount to in 20 yr. at 7%, comp. 14. A father at his death left $12500 for the benefit of his only son, 14 yr. 8 mo. 12 da. old, the money to be paid him when he should be 21 years of age, with 6% interest compounded semi-annually. What did he receive?

ANNUAL INTEREST.

588. Annual Interest is interest on the principal and on each year's interest remaining unpaid, but so computed as not to increase the original principal.

It is allowed in the case of promissory notes and other contracts which contain the words, "with interest payable annually," or with "compound interest." In such cases, the interest is not compounded beyond the second year.

589. 1. Find the annual interest and amount of $8000

“$480 for 10 yr. at 6% = $288. $2400+$288-82688, Annual int. $8000+$2688=$10688, Amount.

ANALYSIS.-The in

terest on $8000 for 1 yr. at 6% is $480, and for 5 yr. is $2400.

The interest for the first year, remaining unpaid, draws interest for 4 yr.; that for the second year, for 3 yr.; that for the third year, for 2 yr.; and that for the fourth year, for 1 yr., the sum of which is equal to the interest of $480 for 4 yr. +3 yr. +2 yr.+1 yr.-10 yr.; and the interest of $480 at 6% for 10 yr. is $288. Hence the total amount of interest is $2400+$288, or $2688, and the amt. is $10688.

2. What is the annual interest of $1500 for 4 yr. at 7%?

RULE.-Compute the interest on the principal for the given time and rate, to which add the interest on each year's interest for the time it has remained unpaid.

To obtain the latter, when the interest has remained unpaid for a number of years, multiply the interest for one year by the product of the number of years and half that number diminished by one.

Thus, if the time is 9 yr., the interest for 1 yr. should be multiplied by 9 × (9-1)+2, or 9 × 436. Since the interest for the first year draws 8 years' interest, that for the second year 7 years' interest, etc., and the sum of the series 8+7+6+5+4+3+2 +1 is 36.

3. What will $3500 amt. to in 10 yr., annual int., at 8% ? 4. What is the difference between the annual interest. and the compound interest of $2500 for 6 yr. at 6% ?

5. Find the amt. of $575, at 8% annual int., for 91 yr.