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COMPOUND INTEREST, Is when the interest is added to the principal, at the end of the year, and on the amount the interest cast for another year, and added again, and so on : this is called Interext upon Interest.
RULE. Find the interest for a year, and add it to the principal, which call the amount for the first year; find the interest of this amount, which add as before, for the amount of the second, and so on for any number of years required. Subtract the original principal from the last amount, and the remainder will be the Compound Interest for the whole time.
EXAMPLES 1. Required the amount of 100 dollars for 3 years at 6 per cent. per annum, compound interest ? $ cts,
Scts. 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 119,1016 for 3 yes. Ans.
2. What is the ancunt of 425 dollars, for 4 years, at 5 per cent. per annum, compound interest ?
Ans. $516, 59cfs. 5. What will 4001. amount to, in 4 years, at 6 percent. per annum, compound interest: Ans. £,504 19š. 9;d. 4. What is the compound interest of 150l. 10s. for 3
ins. 498 14s. 111d. 5. What is the compound interest of 500 dollars for 4 Fears, at 6 per cent. per annu:n : Ans. 8131,258
6. What will 1000 dollars amount io in 4 years, at 7 per cent per annum, compound interest:
ins. $1310, 79c!s. Om.t ht. What is the amount of 750 dollars for 4 years, at 6 per cent. per annum, compound interest ?
Axs. $946, 85cts. 7,721. 8. What is the compound iuterest of 876 dols. 90 cts. for 32 years, at 6
Ans. $198, 8Gcts.
years, at 6
DISCOUNT, Is an allowance made for the payment of any sum of money before it becomes due; or upon advancing ready money for notes, bilis, &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 tiine, anount 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 tine : : so is the river sa!! : to the discount.
Subtract the discount fro! the given sum, and the remainder is the present worth.
Or as the amouut of 100 : is to 100 : : so is the given sum or debt : to the present worth.
Proor. 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 really payment of 100 dollars, due a year lence at 6 per cent: a year?
$ $ 8 $ cts.
100,00 given sum.
SH4,34 the present worth. 2. What sum in realy money will discharge a debt of 925l. due 1 year ani 8 months hence, at 6 per cent. :
10 Interest for 20 months,
110 Am't. £.
. As 110 : 100 :: 925 : 840 18 24 ins. 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 275l. 10s. for 10 months, at 6 per cent. per annum ? 915. f1s 2s. 44
5. Bought gouls amounting to 615 dols. 75 cents, it months creillt; how much ready money must I pay, dis. count at 45 per cent. per annum? Ins. 8000.
6. What sum of ready money must be received for it bill of 900 dollars, due 73 days hence, discount at 6 per cent. per annum ?
Ans. $899, 32cts. 8m. NOTE. When sundry sums are to be paid at different times, find the Rebate or present worth of cach particular payment separately, and when so found, add them into
5. 191:+1the discount of 7561. the one half
payable ir six !!onths, and the other half in six months after that, in parcerias
Ans. £37 10s. 24. 8. If a legacy is left ine of 2000 dollars, of which 500 tluls. are payable in 6 montis, 800 dols. payable in 1 year, and the rest at the end of S years; how much ready money ought I to receive for sarci legacy, allowing per cent. discount:
Bus. $1833, 57cts. 41.
ANNUITIES.CA AN Annuity is a sum of mouey, payable every year, or for a certain number of years, or forerer.
When the debtor keeps the annuity in his own hands, heyond the time of payment, it is said to be in arrcars.
The sum of all the annuities for the time they have been forborne, together with the interesteine on adh, is called the amount.
If an annuity is bougit est, or paid all at once at the beginning of the first year, the price which is paid for it is called the present wortii. To find the amount ol' an annuity at simple interest.
RULE. 1 Find the interest of the given annuity for 1 year.
9. And then for 2, 3, &c. years, up to the given time, less 1.
9. Multiply the annuity hy the number of years given and add the prodluct to the whole interest, and the sum will be the amount sought.
1. If an annuity of 701. be forborne 5 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?
Ir. , £. s. ist. Interest of 701. at 5,
1-3 10 2h 0 3-10 10.
4-14 0 2d. An 5 yrs. annuity, at 70l. per yr. is '
Ins. £5854 2. A house being let upon a lease of 7 years, at 400 dollars per annum, and the rent ling in arrear for the whole term, I demand the sun due at the chil of the term, simple interest being allowed at 6l. per cent. per annum?
To find the present worth of an annuity at simple interest.
1, RULE. Find the present worth of each year by itself, discounting from the time it falls due, and the sun of all these present worths will be the present worth required.
EXAMPLES. 1. What is the present worth of 400 dols. per annun, to continue 4 years, at 6 per cent. per annum? 106
377,35849 Pres. worth of 1st yr. 112 : 100 :: 400:
2d yr. sd yr.
ars. $1396,06503=$1996, Octs. $14. 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. 111. 8. What is 80l. yearly rent, to continue 5 years, worth in ready money, at 6l. per cent. Ans. £,840 155. -+7
QUATION OF PAYMENTS, Is inding 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 by the whole debt, and the quotient will be the equated time for the payment of the whole.
1. A owes B 580 dollars, to be paid as follows- viz. 100 dallars 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 ?
6 600 120 X
hvort 840 160 x 10 1600
5040(8 months. Ans. A merchant hath owing him 300l. to be paid as foliows: 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 II 1000 dollars, whereof 200 dollars is to be paid present, 400 dollars at 5 months, and the rest at 15 inonths, but they agree to make one payment of the whole; i demand when that time must be ? Ans. 8 months.
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, and the rest at 6 months ; what is the equated time for the payment of the whole ? Ans. 4 months.
the exchanging of one commodity for another, and directs merchants and traders how to make the exchange vithout loss to either party.
RULE. Eind the value of the commodity whose quantity is giren ; then find what quantity of the other at the pro