2. What is the present worth of $2240 due in 2 years, discount at 6 per cent.? What is the discount?

3. How much READY MONEY should I receive on a note for $257.28, due in 1 year, 2 months, 12 days, at 6 per cent. discount?

4. What DISCOUNT should be allowed for the ready payment of $658.62, due in 3 years, 7 months, 18 days, at 6 per cent. PER ANNUM?

5. A retailer purchased goods in Philadelphia, amounting to $2500, on which he paid cash, and gave his note for the balance, which would become due in 11 months; how much READY MONEY would pay the balance?

5. What sum of ready money will discharge a debt of $4582.68, due in 4 years, 7 months, and 23 days, allowing discount at 6 per cent. PER ANNUM?

EQUATION OF PAYMENTS.

EQUATION OF PAYMENTS is that process by which we ascertain ONE PERIOD for making several payments, which are due at different times.

EXAMPLES.

1. A merchant has four notes against the same person, the first calls for $300, which is due in 2 months; the second, $250, due in 4 months; the third, $200, due in 3 months; and the fourth, $150, due in 6 months, in what time will the whole be due?

Analyze thus: first, the interest of $300 for 2 months, is the same as the interest of $1 for 300 times 2 months to 600 months. Second, $250 for 4 months equals $1 for 250 times 4 months to 1000 months. Third, $200 for 3 months, is the same as $1 for 200 times 3 months = to 600 months; and, fourth, $150 for 6 months, is the same as $1 for 150 times 6 months equal to 900 months. Now, 600 mo.+1000 mo. + 600 mo. + 900 mo. = 3100 months and $300+ $250+$200+ $150 = $900, and since the equated interest of $1 requires 3100 months, it follows inversely, that the equated interest of $900 will require of 3100 months

1st, the inst. of 300 for 2=the inst. of 1 for 300 times 2= 600

2. A merchant holds six obligations against the same person, as follows: first, $250, due 3 months ago; second, $350, due 2 months ago; third, $500, due 1 month ago; fourth, $400, due 1 month hence; fifth, $500, due in 4 months; sixth, $400, due in 5 months, in what time will the whole be due?

mo. $.

mo. months. 250 for 3=1 for 250 times 3= 750 350 66 2=1 66 350 66 2= 700

After deducting the back time, we find that the future time exceeds by 2450 months, i. e., the time for which $1 must be on interest, exceeds the time for which it has been on interest by 2450 months. The question, therefore, is, if $1 has 2450 months to run, how long will $2400 have to run?

3. A. holds 4 notes against B., due as follows: $250, due 4 months ago; $300 due 2 months ago; $150 due in 2 months; and $350, due in 4 months. B. wishes to pay the whole now; what sum will discharge them, allowing discount or interest, as the case may be, at 6 per cent.? Thus:

250 for 4 1 for 250 times 4 =1000

"21" 300 66

mo. months.

months.

300

2= 750=1750

From which it appears, that $1 must be discounted for 50 months, and hence, inversely, $1050 must be discounted for 1050 of 50 months to 5 of a month = to

50

of a month = to 3 of a day = to 127, or 12 of a day, the PRESENT worth for which time, at 6 per cent., is 4200 of $1050 = to $1049.75+. ANSWER.

dated

4. A wholesale merchant has a running account with a retailer, consisting of the following items, viz. first, $325.18, dated March 4th, 1840; second, $268.50, dated May 12th, 1840; third, $464.48, dated September 18th, 1840; fourth, $268.74, dated December 14th, 1840; fifth, $568.42, February 23d, 1841; sixth, on the 20th of April, 1841, the latter purchased goods amounting to $564.72, and at the same time settled the whole account; what should he pay, allowing 4 months' credit to each item in the account, and the usual discount, or interest, as the case may require?

Solution.-The first purchase, $325.18, has been standing from March 4th, 1840, to April 20th, 1841, making ly. Imo. 16da., equal to 406 days, from which take the credit, 4 months to 120 days, and there remains 286 days, for which interest should be calculated; the second purchase,

$268.50, has been due 218 days; the third, $464.48, has been due 92 days; the fourth, $268.74, has been due 6 days; the fifth, $568.42, will not be due for 63 days, for which discount should be allowed; and the sixth, $564.72, will not be due for 4 months, or 120 days, all of which may be equated as follows, viz.

Inst. of 325.18 for 286=inst. of 1 for 93001.48

days.

"35810.46

Dis't. of 568.42 " 63 dis't. of 1

66 564.72" 120= 66 1 "67766.40=103576.86

2460.04

92302.22

100 246004 · 100 ̄ ̄ 123002

The wholesale merchant is, therefore, entitled to 37 days' interest on the whole debt, which amounts to 12075 of $24 246004 to $2475.415. ANSWER.

The preceding examples, if properly studied will sufficiently illustrate the following

RULE for Equating Payments.

Multiply each payment by its TIME (in the same denomination,) and divide the sum of these products by the sum of the payments, the QUOTIENT will be the EQUATED TIME in months if the time of the payments were months, or days, if days, &c.

NOTE.-From the examples given, we also learn, that when several notes, or other obligations are to be paid at a certain date, and the same, or different credits are allowed on each, we must first find the TIME from the date of each obligation, to the date of final settlement, from WHICH We must deduct the time for which credit is allowed, when the

FORMER will admit of it, but when it will not, we must deduct the FORMER from the latter, and in either case multiply the payment by the difference, by which process we will obtain two classes of PRODUCTS repugnant to EACH OTHER, i. e., one class of products, in favor of the CREDITOR, but the other in favor of the DEBTOR; to distinguish these, we call the sum of the products in favor of the creditor, a PLUS quantity, but the SUM of the products in favor of the debtor, a MINUS quantity. Again, since these PLUS and MINUS quantities have reference to the character of the multipliers which produced the several PRODUCTS Composing THEM, and since these multipliers are found either by subtracting the TIME of credit from the TIME between the DATE of purchase and that of final settlement, or vice versa, it is plain, that when the TIME from the date of the obligation to final settlement, is greater than the TIME of credit, the difference will be in favor of the creditor, and may, therefore, be termed POSITIVE, thus constituting a POSITIVE multiplier; but when the TIME of credit exceeds the TIME from the date of obligation to that of final settlement, the DIFFERENCE will be in favor of the debtor, and may, therefore, be termed NEGATIVE, thus constituting a NEGATIVE multiplier. These quantities, the learner should be careful to distinguish, it will then become evident that,

First. A POSITIVE multiplier will produce a PLUS product. Second. A NEGATIVE multiplier will give a MINUS product. Third. If the PLUS products be added, their SUM will be a PLUS quantity, in favor of the creditor; and,

Fourth. If the MINUS products be added, their sum will be a MINUS quantity, in favor of the debtor.

Fifth. When the EXCESS is in favor of the creditor, the EQUATED TIME shows the PERIOD for WHICH he must be allowed interest on his entire claim, the amount of which, for the time, will be the ANSWER; and,

Sixth. If the DIFFERENCE is in favor of the debtor, the EQUATED TIME is the PERIOD for WHICH he can claim LEGAL DISCOUNT on the WHOLE AMOUNT of his indebtedness, the present worth of which, for that time, will be the ANSWER.