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COMPOUND INTEREST Is when the interest is added to the principal, at the end of the year, and on that amount the interest cast for ạnother
year, and added again, and so on : this is called Interest upon Interest.
RULE. Find the interest for a year, and add it to the princi. pal, which call the amount for the first ; find the interest of this amount, which add as before, for the amount of the second, and so on for any number of years re. quired. Subtract the original principal from the last amount, and the remainder will be the Compound Interest for the whole time.
1. Required the amount of 100 dollars for 3 years, at 6 per cent. pėr annun, compound interest ?
$ cis. Ist Principal 100,00 Amount 106,00 for 1 year. 2d Principal 106,00 Amount 112,36 for 2 years. 3d Principal 112,36 Amount 119,1616 for 3 yrs, Ans.
2.. What is the amount of 425 dollárs, for 4 years, at 5 per cent. per annum, compound interest?
59cis. 3. What will 4001. amount to, in four years, at 6 per cent. per annum, compound interesi ?
Ans. £504 19s.-93d. 4. What is the compound interest of 1501. 10s. for 3 years, at 6 per ct. per annum ? Ans. £28 14s. 114d.+
5. What is the compound interest of 500 dollars for 4 years, at 6 per cent. per annum ? Ans. $131,238+
6. What will 1000 dollars amount to in 4 years, at 7 per cent. per annum, compound interest ?
Ans. $1310, 79c1s. 6m. + 7. What is the amount of 750 dollars for 4 years, at 6 per cent. per annum, compound interest ?
ins. $946, 85cis. 7,72m. 8. What is the compound interest of 376 duls. 90 ctx. for 3 years, at 6 per cent per annum?
Ans. $198, 83cts.
DISCOUNT, Is allowance made for the payment of any sum of 3 money before it becomes due; or upon advancing ready money for notes, bills, &c. which are payable at a future day. What remains after the discount is deducted, is the present worth, or such a sum as, if put to interest, would at the given rate and time, amount to the given sum or debt.
RULE. As the amount of 100l. or 100 dollars, at the given rate and time : is to the interest of 100, at the same rate and time : : so is the given sum: to the discount. Subtract the discount from the given sum,
and the remainder is the present worth.
Or—as the amount of 100 : is to 100 : : so is the given sum or debt : to the present worth.
Proof.- Find the amount of the present worth, at the given rate and time, and if the work is right, that will be equal to the given sum.
1. What must be discounted for the ready payment of 100 dollars, due a year hence at 5 per cent. a year?
100,00 giren sum.
$94,34 the present worth. 2. What sum in ready money will discharge a debt of 925l. due 1 year and 8 months hence, at 6 per cent, ? £100
10 Interest for 20 months.
110 Am't. £. £. £. £. a.
As 110: 100 :: 925 : 840 18 2 + Ans. 3. What is the present worth of 600 dollars, due 4 years hence, at 5 per cent. ?
Ans. $500 4. What is the discount of 2751. 10s. for 10 months, at 6 per cent. per annum ? Ans. £13 2s. 41..
5. Bought goods amounting to 615 dols. 75 cents, at 7 months credit ; how much ready money must I pay,
discount at 41 per cent. per annum ?
Ans. $600. 6. What sum of ready money must be received for a bill of 900 dollars, due 73 day's hence, discount at 6 per cent. per annum ?
Ans. $889, 32cts. Sm. Note-When sundry sums are to be paid at different times, find the Rebate or present worth of each particular payment separately, and when so found, add them
into one sum. Р e
7. What is the discount of 758. the one half payable in six months, and the other half in six months after that, at 7 per cent. ?
Ans. £37 l0s. 2 d. 8. If a legacy is left me of 2000 dollars, of which 500 dols. are payable in 6 months, 800 dols payable in 1 year, and the rest at the end of 3 years ; how much ready money ought I to receive for sais legacy, allowing 6 per cent. discount !
Ans. $1833, 37cts. 4m.
ANNUITIES. AN Annuity is a sum of money, payable every year, or for a certain number of years, or for ever.
When the debtor keeps the annuity in his own hands beyond the time of payınent, it is said to be in arrears.
The sum of all the annuities for the time they have been foreborne, together with interest due on each, is called the amount.
If an annuity is bought off, or paid all at once at the beginning of the first year, the price which is paid for it is called the present worth. To Find the amount of an annuity at simple interest.
2. And then for 2, 3, &c. years, up to the given time, less 1.
3. Multiply the annuity by the number of years giv, en, and add the product to the whole interest, and the sum will be the amount sought.
1. If an annuity of 701. be forborne 3 years, what will be due for the principal and interest at the end of said term, simple interest being computed at 5 per cent. per annum ?
Yr. £. s. Ist. Interest of 701. at 5 per cent. for 1- 3 10
20 3-10 10
414 0 2d. And 5 yrs. annuity, at 70l. per yr. is 350 0
Ans. £385 0 2. A house being let upon a lease of 7 years, at 400 dollars per annum, and the rent being in arrear for the whole term, I demand the sum due at the end of the term, simple interest being allowed at 6l. per cent. per annum 3
To find the present worth of an annuity at simple interest.
RULE. Find the present worth of each year by itself, discounting from the time it falls due, and the sum of all these present worths will be the present worth required.
EXAMPLES. 1. What is the present worth of 400 dols. per annum, to continue 4 years, at 6 per cent, per annurn? 106
Pres. worth of 1st yr. 112
357,14285 :100: : 400 : 118
2d yr. 3d yr. 4th yr.
Ans. $1396,06508 =$1396, 6cts. 5m. 2. How much present money is equivalent to an annuity of 100 dollars, to continue 3 years ; rebate being made at 6 per cent. ?
Ans. $268, 37cts. Im. 3. What is 80l. yearly rent, to continue 5 years, worth in ready money, at bl. per cent ? Ans. £340 158. +
EQUATION OF PAYMENTS, S finding the equated time to pay at once, several debts due at different periods of time, so that no loss shall be sustained by either party.
RULE. Multiply each payment by its time, and divide the sum of the several products hy the whole debt, and the quotient will be the equated time for the payment of the whole.
EXAMPLES. 1. A owes B 380 dollars, to be paid as follows-viz. 100 dollars in 6 months, 120 dollars in 7 months, and 160 dollars in 10 months; What is the equated time for the payment of the whole debt ?
100 X 6 600
)3040(8 months. Ans. 2. A merchant hath owing him 3001. to be paid as fol. lows: 501. at 2 months, 1001. at 5 months, and the rest at 8 months; and it is agreed to make one payment of the whole ; I demand the equated time? Ans, 6 months.
3. F owes H 1000 dollars, whereof 200 dollars is to be paid present, 400 dollars at 5 months, and the rest 15 months, but they agree to make one payment of the whole; I demand when that time must be ? Ans. 8 monihs.
4. A merchant has due to him a certain sum of money, to be paid one sixth at 2 months, one third at 3 months, Ind the rest at 6 months ; what is the equated time for the payment of the whole?
Ans. 4; monihs.
S the exchanging of one conamodity for another, and directs merchants and traders how to make the exchange without loss to either party.
RULE. Find the value of the commodity whose quantity is giren; then find what quantity of the other at the proposed