PROBLEMS IN INTEREST.

576. Interest, time, and rate given, to find the principal.

1. What sum of money will gain $10 in 1 yr. at 5%?

ANALYSIS.—The interest of $1 for 1 yr. at 5% is .05 of the prin cipal, and therefore $10.05, or $200, is the required sum. Or, Since $.05 is the interest of $1, $10 is the interest of as many dollars as $.05 is contained times in $10, or 200 times. Hence, etc.

577. 1. What sum of money, put at interest 31 yr. at 6%, will gain $346.50?

OPERATION.

Int. of $1 for 3 yr. at 6% = $.21.

$346.50$.21 1650 times;

$1 × 1650 = $1650.

What principal

ANALYSIS.-Same as in

oral exercises. (576.)

2. Will gain $49.50 in 1 yr. 3 mo. at 6%? At 5% ? 3. Will gain $153.75 in 3 mo. 24 da. at 7%? At 8%?

RULE.-Divide the given interest by the interest of $1 for the given time, at the given rate.

FORMULA.-Principal = Interest ÷ (Rate × Time).

What sum of money

4. Will gain $213 in 5 yr. 10 mo. 20 da. at 7%?

5. Will gain $173.97 in 4 yr. 4 mo. at 6%? At 12% ?

6. A man receives semi-annually $350 int. on a mortgage at 7% What is the amount of the mortgage?

578. Amount, rate, and time given, to find the principal.

1. What sum of money will amount to $107 in 1 yr.

at 7%?

ANALYSIS. Since the interest is .07 of the principal, the amount is 1.07, or 18, of it. If $107 is 187 of the principal, of the principal is of $107, or $1; and 188, or the principal itself, is $100. Or, Since $1.07 is the amount of $1, $107 is the amount of as many dollars as $1.07 is contained times in $107, or $100.

579. 1. What sum will amount to $337.50 in 5 yr.

at 7%?

OPERATION.

Am't of $1 for 5 yr. at 7% = $1.35.

$337.50 $1.35 = 250 times;

$1 x 250 = $250.

What principal

ANALYSIS. Same as

in oral exercises. (578.)

2. Will amount to $1028 in 4 mo. 24 da. at 7%?

3. Will amount to $1596 in 2 yr. 6 mo. at 51% ?

4. Will amount to $1531.50 in 3 mo. 18 da. at 7%?

RULE.-Divide the given amount by the amount of $1 for the given time, at the given rate.

FORMULA.-Prin. = Amt. ÷ (1 + Rate × Time).

5. What is the principal which in 217 days, at 51%, amounts to $918.73 ?

6. What principal in 3 yr. 4 mo. 24 da. will amount to $761.44 at 5%?

580. Principal, interest, and time given, to find the rate.

1. At what rate will $100 gain $14 in 2 years?

ANALYSIS. Since the interest of $100 is $14 for 2 yr., it is $7 for 1 yr., and $7 is .07 of $100, the principal. Hence the rate is 7%. Or, Since the interest of $100 for 2 yr. at 1% is $2, $14 is as many per cent. as $2 is contained times in $14, or 7%.

581. 1. At what rate per cent. will $1600 gain $280 interest in 2 years?

2. Will $2085 gain $68.11 in 5 mo. 18 da. ?

3. Will $1500 gain $252 in 2 yr. 4 mo. 24 da. ?

RULE.-Divide the given interest by the interest of the

given principal, for the given time, at 1%.

FORMULA.-Rate Int. ÷ (Prin. x 1% x Time).

4. A house that cost $14500 rents for $1189. What per cent. does it pay on the investment?

5. At what rate will $1500 amount to $1684.50 in 2 yr. 18 da. ?

6. At what rate per month will $2000 gain $120 in 90 da. ?

7. A man invests $15600, which gives him an annual income of $1620. What rate of interest does he receive?

8. At what rate per annum will any sum double itself in 4, 6, 8, and 10 years, respectively?

At 1%, any sum will double itself in 100 yr.; hence, to double itself in 4 yr., the rate will be as many times 1% as 4 yr. are contained times in 100 yr,, or 25%, etc.

9. At what rate per annum will any sum triple itself in 2, 5, 7, 12, and 20 years, respectively?

10. I invest $49500 in a business that pays me $297 a month. What annual rate of interest do I receive?

11. Which is the better investment, and how much, one of $4200, yielding $168 semi-annually, or one of $7500, producing $7124 annually?

582. Principal, interest, and rate given, to find the time.

1. In what time will $200 gain $56 at 7%?

ANALYSIS.-The given interest, $56, is 5%, or .28, of the princi pal, $200; therefore, the time is as many years as .07, the given rate, is contained times in .28, or 4 times. Hence, etc.

Or, the interest of $200 at 7% for 1 yr. is $14; therefore, the time is as many years as $14 are contained times in the given interest, $56, or 4 years. Hence, etc.

In what time will 2. $40 gain $10 at 5%? 3. $500 gain $100 at 4%? 4. $25 gain $20 at 6% ?

WRITTEN

5. $1000 gain $250 at 5%? 6. $5 gain 90 cents at 6% ? 7. $50 gain $12 at 10%?

EXERCISES.

583. 1. In what time will $840 gain $78.12 at 6% ?

2. Will $175.12 gain $6.43 at 6% ?

3. Will $1000 amount to $1500 at 71%?

RULE.-Divide the given interest by the interest of the given principal, at the given rate for 1 year.

FORMULA.-Time

Interest÷(Prin. x Rate).

4. In what time will $8750 gain $1260 at 2% a month? 5. How long must $1301.64 be on interest to amount to $1522.92 at 5%?

6. How long will it take any sum of money to double itself at 3%, 5%, 6%, 7%, and 10%, respectively?

At 100%, any sum of money will double itself in 1 year; hence to double itself at 10%, it will require as many years as 10% is contained times in 100%, or 10 yr.

7. How long will it take any sum to triple itself at 1%, 5%, 7%, 8%, and 121%, respectively?

8. In what time will the interest of $120, at 8%, equal the principal? Equal half the principal? Equal twice the principal?