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CHAPTER XII

APPLICATIONS OF PERCENTAGE_WITH TIME

I. SIMPLE INTEREST

334. In this chapter the applications of percentage contain the element of time.

335. Interest is money charged for the use of money.

336. The principal is the money for the use of which interest is charged.

337. The time is the period during which the principal bears interest.

338. The amount is the sum of the principal and the interest.

339. The rate of interest is the per cent to be taken of the principal for one interval of time.

NOTE 1.-The rate per cent means the rate per cent per annum unless some other period of time is specified.

NOTE 2.-The legal rate is the rate established by law, and is always understood when no rate is specified in a contract.

The contract rate is the maximum rate permitted by law when specified in a contract. Legal and contract rates vary.

Usury is any rate higher than the contract rate.

340. Simple interest is the interest on the principal only. It is found by taking the continued product of the principal by the rate by the time expressed in years. Using the initial letters, we have the formula: I = P X R X T.

NOTE. - In the following table, G represents 3 days of grace ; P, previous business day; S, succeeding business day.

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EXAMPLES

1. Find the interest of $450 for 120 days at 8%.

SOLUTION BY FORMULA :
Since I = P x R x T, .. I $450 X Too x

= $12.

SOLUTION BY ANALYSIS :

1. Since 100% of principal = $450, I. 2. .. 1%

Too of $450 $4.50. 3. and 8%

8 * $4.50 = $36,= int. for 1 yr. 1. Since int. for 360 days $36, II. 2.

int. for 1 day do of $36 $0.1, 3. and int. for 120 days 120 x $0.1 $12. NOTE.-In ordinary business transactions, 30 days are considered a month, and 360 days a year.

Using the formula above, make a formula for finding the principal, the rate, and the time. Write the rule for each formula made.

2. At what rate will $360 produce $24 interest in 1 year and 4 months?

SOLUTION :

I
Since I = P x R x TR

PX T

$24 Substituting: R =

$360 x 1}

.05, or 5%.

$24,

I.

int. for 1 yr.

ANALYSIS:
1. Since int. for 1 yr. 4 mo., or $ yr.,
2. ..

of $24 $18.
1. Since $360 = 100% of the principal,
2. ... $1 = zty of 100% = %% of the principal,
3. and $18 = 18 × %, or 5% of the principal.

... the rate = 5%.

II.

::T

3. In what time will $480 produce $60 at 5%?

SOLUTION:
I

$60
Since T

- 21, or 2} yr. Px R

$480 x .05 NOTE.—The solution by the formula is purely mechanical. It will do for commercial purposes, but for educational purposes the solution by analysis is far more valuable.

ANALYSIS : 1. Since 100% of prin. I. 2. ... 1%

Too of $480 3. and 5%

5 x $4.80 = $24.

$480,

$4.80,

66

66

II.

1. Since $24 is the int. for 1 yr.,
2. .. $1
3. and $60

" 60 24 yr., or 24 yr.

66 24 yr.,

1% "

$0.01,

$0.06,

4. What principal will amount to $2394 in 2 years and 4 months at 6%?

SOLUTION :

Assume $1 as a principal. 1. Since 100% of prin. $1, I. 2. ..

Too of $1 3. and 6%

6 x $0.01 = $0.06. 1. Since the int. for 1 yr. II. 2. .. the int. for } yr. = } $0.06 = $0.14.

3. Now, $1 + $0.14 $1.14, am’t of $1 for 2 yr. 4 mo.

1. Since $1.14 am't requires $1 prin., III. 2. .. $1

$1. prin., 3. and $2394

2394 * $1.14 prin.=$2100 prin.

SHORT PROCESS :
1. Int. on $1 for 2 yr. 4 mo. at 6% $0.14.
2. Am't of $1 for 2 yr. 4 mo. at 6% $1.14.

3. $2394 + $1.14 2100... $2100 is the prin. NOTE.-By means of the solution above, the present worth of a debt is found.

341. The present worth of a debt payable at a future date without interest is that sum which, when put on interest for the time yet to elapse, will amount to the debt.

The above example might be stated thus: What is the present worth of $2394, due 2 yr. 4 mo. hence, money being worth 6%, simple interest?

342. The true discount is the difference between the debt and the present worth. It is, therefore, the simple interest on the present worth.

5. Find the present worth and true discount of a debt of $627 due in 9 months, money being worth 6%.

SOLUTION:
Present worth

A
$627 $627

$600. 1 + R XT 1 + Too xia

$627 - $600 $27, true discount. The meaning is: $600 put on interest at 6% for 9 mo. would amount to $627.

Solve this problem by analysis, following the form in example 4 above.

NOTE.-In true discount, it is not customary to allow 3 days

of grace.

343. In bankers' interest (bank discount), the exact number of days is counted; but, in expressing the time in years, 360 days is considered 1 year. Thus, the time from May 2, 1904, to August 5, 1904, is 95 days, or 30 yr.

344. In exact interest, the exact number of days is counted; but, in expressing the time in years, 365 days is considered 1 year (366 days in leap years). Thus, the time from January 1, 1904, to July 12, 1904, is 193 days, or 388 yr.

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