When interest is at 7, 10, 11, &c. per cent. it will be most convenient, first to find the interest at some rate which is an aliquot part of 12, and then take parts for the remaining part of such rate.

The interest may also be had when the rate is 7, 11, &c. per cent. by multiplying the principal by the rate per cent. and by the time in months; and dividing the result by 12, and by 100. Because,

PR

100

the interest of P for one year;

Observing always, that if any of the quantities represented by P, R, or T, be divided by 12, or by 100, before they are multiplied together, the work will be shortened,

THEOREM 3.

The Legislature of Pennsylvania, in passing laws to incorporate and charter the several companies for the purpose of banking, in this state, having authorised these several institutions to exact from their customers, who borrow money from them, on all loans at the rate of one per cent. for 60 days; and interest is now universally charged at this rate in all the

banks of the state.

Hence, this rule of calculating interest has become the law of the state; and certainly, no reason exists, why every citizen of the state should not have the same privilege that is specially granted to these banking institutions; especially when the time is less than

a year.

Hence, we deduce this useful theorem, for calcu lating interest for days, at 6 per cent.

Putting Pany given principal, and T=any given time in days; then we shall have,

Now this theorem expressed in words, reads thus:

Multiply the given principal by the given days, divide the product by 6, and cut off three places for decimals on the right hand, and you have the interest required.

NOTE. It is evident by inspection, that, when T, the number of the given days, or P, the principal, happen to be either a part or a multiple of the denominator 6, or 100, the work will be shortened, by dividing such fators as will measure each other, by any common divisor.

It is also evident, that this theorem furnishes the shortest general rule possible, for calculating simple: interest for days.

COMPOUND INTEREST.

Compound Interest, or interest upon interest, is scarcely used in business; we shall therefore give but one or two examples, to shew how it is calculated.

EXAMPLE.

What is the compound interest of $3475 for 3 years, at 6 per cent per annum?

3475 1.06 x 1.06 x 1.06=4138.7806=amount,

and 4138.7806—3475—664.7806=interest.

If r=1.06 amount of 1£. or 18. for 1 year, p=principal,

i=interest,
t=time,

a=amount,

The following theorems shew the method of resolving all the cases of Compound interest, except t, which must be found by logarithms, viz.

To find the interest of $3475 according to theorem 2d, on the preceding page.

3475×1.063-3475-3475×1.191016-3475—

$663.7806 Answer.

To find the amount, $3475x1.06=4138.7806 Ans.

amount of $1 for 1 year, and 1.06-1.06—8=rate

per cent 6 for 100.

To find the time,

Log. 4138.7806--Log. 3475
Log. 1.06

=3. Ans.

For

Log. a.-Log. pt. as is shewn further on.
Log. R.

REBATE OR DISCOUNT.

Discount is an allowance made for the payment of money before it is due; which allowance is less than common interest for the time, by the interest of the interest.

The balance, after discount is deducted, is called the present worth.

If the present worth be put to interest, at the rate per cent and for the time, the amount will be equal to the sum which would have then been due by the obligation..

To find the discount of

any sum of money for one

year,

RULE.

Multiply the sum by the rate per cent, and divide by a hundred more the rate per cent, and the thing is done.

EXAMPLES.

1. Find the discount of $375, due one year hence, at 6 per cent.

106: 6: 375 : 21.223 Ans.

2. Find the discount of $3754.40, due 1 year hence, at 6 per cent. Ans, $212.517.

To find the present worth of any sum for one year,

RULE

Multiply the sum by 100, and divide by 100 more than the rate per cent, and the thing is done.

EXAMPLES.

1. Find the present worth of $1760, due 1 year hence, at 6 per cent.

106 100 1760: 1660.37 Ans.

:

2. Find the present worth of a bond for $1000, due 1 year hence, at 6 per cent. Ans. $943.3933.

To find the present worth of a note or bond, due 2, 3 or more years hence,

RULE.

Divide the given sum by the product of the time and ratio more 1, and the thing is done.