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REM.-In the computation of interest we find the interest equal to the product of the principal, rate per cent, and time. By using the initial letters for these, we get convenient formulas; thus,

Let P =
I = interest; we have the equation

Pxrxt = I.

principal, r rate per cent, t = time, and

(1.)

Divide both members by r x t,

I

(2.)

P =

Principal equal to interest divided by the product of rate and time.

(3.)

Rate equal to interest divided by the product of principal and time.

(4.)

Time equal to interest divided by the product of principal and rate.

r =

t =

rx t

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I
Pxt

I
Px r

ENUNCIATION OF THE FORMULAS.

1. The interest of a sum of money is equal to the called principal, multiplied by the rate and the time.

sum,

2. The principal is equal to the interest divided by the product of the rate and the time.

3. The rate is equal to the interest divided by the product of the principal and the time, and then reduced to hundredths.

4. The time is equal to the interest divided by the product of the principal and the rate.

The four formulas enable us to determine any one of the four quantities when the other three are known.

PROBLEMS.

1ST FORMULA. The principal is $750, the rate 6%, time 8 months. What is the interest?

I = $750 × 100 X

P =

2D FORMULA.-The interest is $30, the rate 6%, and the time 8 months. What is the principal?

$30

30

4

8 4
100 X 12 100

2

r =

4TH FORMULA.

t =

$30 750 × 12

3D FORMULA.-The interest is $30, the principal $750, and the time 8 months. What is the rate?

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= 30x100 $750, Principal.

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=

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2 ==, Time.

EXAMPLES.

1. Compute the interest on $5464.50, at 5%, for 1 year 9 months and 18 days. Ans. $491.805.

2. Compute the interest on $5464.50, at 8%, for 1 year 9 months and 18 days. Ans. $786.888.

3. Compute the interest on $5464.50, at 10%, for

1 year 9 months and 18 days?

4. The interest is $630, the rate 18 months. What is the principal ?

5. The interest is $540, the rate 24 months. What is the principal?

6. The interest is $600, the rate 5%, 30 months. What is the principal ?

7. The interest is $300, the principal the time 30 months. What is the rate?

=

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8. The interest is $560, the principal $3000, and the time 32 months. What is the rate? Ans. 1%.

9. The interest is $140, the principal $1500, and the time 16 months. What is the rate?

10. The interest is $270, the principal $3000, and the rate 6%. What is the time? Ans. 1 years.

11. The interest is $360, the principal $2400, and the rate 8%. What is the time? Ans. 224 months.

12. The interest is $66, the principal $500, and the rate 6%. What is the time?

13. The principal is $440, the interest $88, and the time 4 years. What is the rate? Ans. 5%.

14. The principal is $650, the interest $78, and the rate 6%. What is the time? Ans. 2 years.

15. The interest is $48, the rate 4%, and the time. 3 years. What is the principal? Ans. $400.

16. In what time will any sum of money double itself at 6% simple interest?

I

P

t =

xr

Pxr

REM.-When the principal is doubled, the interest is equal to the principal; that is, I = P.

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=

1

6

100

6%, and the time
Ans. $7000.
9%, and the time
Ans. $3000.
and the time

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$2400, and Ans. 5%.

1x 100 = 163 years.

BANKING.

Bank Discount is reckoned on the face of the note the same as interest.

It is called discount, as the interest for the time the note is given and three days grace is deducted from the face of the note, and the borrower receives the difference. A note in bank is not considered due until three days after the time specified.

The bank discount on a rate for

5

$100 at 60 days = 100 × 8 × M = £1 = $1.05.

&a

Proceeds $100 $1.05 $98.95.

$100 at 90 days
Proceeds $100 $1.55 $98.45.

25

$500 at 90 days = 500 × 8 × 32% = }} = $7.75.

93 360

& a

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93

= 100 × råa × g = H = $1.55.

*

& &

Proceeds $500 - $7.75 = $492.25.

162

$324 at 90 days = $24 × 3 == $5.022.

31 2008

1000

Produce $324 $5.02 $318.98.

A bank account is closed at the end of the year, and the next year is begun by bringing forward the balance which belongs to the credit side of account, as overdrawing is not permitted.

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To this balance each deposit is added at the date on which it is made, and from the sum on the credit side is subtracted each sum drawn by check at its date.

Each sum or balance is multiplied by the number of days from its date until the next transaction; lastly, the difference at the last transaction by the time until the end of the year.

The sum of all these products will be the number of days that one dollar is at interest.

1877.

66 100

Jan. 6. To check. $200
"15. 66
"18. 66
❝ 29. 66

The last sum or difference on the credit side will be the principal.

DR. JAMES KENNEDY in acct. with MERCHANTS' BANK.

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66

200

350

Balance items.
Bal. interest.
Total bal.

CR.

DA.

PRO.

1876.
Dec. 31. By bal. old acct. $600 6 3600
Jan. 10. By cash $300. 400 4 1600
Jan. 25. By cash $750.

700 5

3500

600 3

1800

400 7

2800

4600

1150 4
800 2 1600
3.25 6)19,500

$803.25 Int. 3.25

This account is only read for one month, a repetition would bring it to the end of the year, when the last balance on credit side is the balance in bank at the end of the year, and the deposits with their dates; the debit side shows the sums drawn and their dates, the column of products gives the number of days that one dollar is on interest.

REM.-If a creditor were permitted to overdraw, interest on the balance would be computed on the debit side, and the difference between the two columns of products would belong to the side having the greater sum.

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