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3. At what rate of interest per cent will 420l amount to 5201 153 in 8 years ? Ans. 3 per cent.
CASE 7. Q. How is the time found when the principal, amount and rate per cent are given ?
A. As the interest of the principal for 1 year at the giren rate
Is to one year :
To the time required. 1 In what time will 500l amount to 7251 at 5 per cent per annum ? Aus. 9 years,
2 In what time will 6201 amount to 7931 12s at 4 per cent per annum ? Ans. 7 years.
3 In what time will 4201 aniount to 5201 16s at 3 per cent per annum ? Ans, 8 years.
Q. How are the questions in the foregoing cases proved ? - A. Cases 1, 5, 6, and 7, do exactly prove each other; by varying the questions : yet all of them except case the ist, 2nd, 5th, 6th, and 7th, questions in case 1, and the 6th, 7th, and 8ih, in case 2, may as truly be answered by the double rule of three, of which more hereafter.
Note 1. The 1st. 2nd, 5th, 6th, and 7th, Questions in Case 1, and the 6th, 7th and 8th in Case 2, are to be proved by the rule of three.
2. Case 5th, cannot be answered by the double rule of three, because the principal is not known in the question, and ther fore there can be no deduction of it from the amount, to know the interest, which must first be done.
OF SIMPLE INTEREST FOR
A. Multiply the pence of the principal by the days, and by the rate of interest for a dividend. and 36, by 100 for a divisor. the quotient will be the answer in pence.
Q. How are the following questions proved ?
Are to the interest of a given sum for a year ;
To the interest required. 1 What is the interest of 1201 for 126 days at 4 per cent per annum ? Ans 1l 138 10 2 qrsus.
2. What is the interest of 1261 for 145 days, at 6 per sent per annum ? Ans: 31 us od 3qr 3%.
3. What is the interest of 100l from June 1; 1773, to March 9, 1776, which is Leap Year, at 5 per cent. per annum ? Ans. 31 17s 6d 1
qr 4 What is the interest of 2001 from August 14, to December 19 following, at 6 per cent per annun ? Ans. 41 As id sqr
5 What is the interest of 10l for 25 days, at 5 per cent per annum ? Ans. $dzor
6 What is the interest of 401 for 40 days, at 4 per cent per annum ? Ans. 3s 6dzo
See more of Simple Interest in Decimals.
A. Compound Interest is that which arises from any principal and its interest put together, as the interest still becomes due ; and for that reason it is called interest upon interest or compound interest.
Q. Is it lawful to let out money at compound interest ?
A. 1. No: yet in purchasing of annuities or pensions, and leases in reversion. it is very usual to allow compound interest to the purchaser for his ready money and therefore it is very necessary to understand it.
Q. How do you find the compound interest ofany giveu. • sum for any number of years ?
A. 1. Find the amount of the given sum by Simple Inferest for the first year, which is the principal for the second year, then find the amount of that principal for the second year, and that is the principal for the third year; and so on for any number of years given.
2 Subtract the given sum from the last amount, and the remainder is the compound interest required.
1. What sum will 4501 amount to in three years, at 5 per cent per annuin compound interest ? Ans. 5201 185 70.
2 What will 4001 amount to in 4 years, at 6 per cent per annum compound interest ? Ans. 5041 168 9d.
3 What will 4801 amount to in 6 years, at 5 per cent per annum compound interest ? Ans. 6431 45 10d. į
4 What will 500l amount to in 4 years at 44 per cent per annum compound interest ? Ans. 5901 i 18 5d.
5 What is the compound interest of 4001 10s at 31 per cent per annum, for 3 years ? Ans. 431 10s. 9d.
Note. See more of Compound Interest in Decimals.
OF REBATE OR DISCOUNT..
Q. WHAT is Rebate or Discount ?
A. Rebate or Discount is when a sum of Money due at any time to conve, is satisfied by paying so much present money as being put out to interest, would amount to the given sum in the same space of time.
Q. How is the operation performed ?
Are to the Rate per Cent,
To a fourth Number.
Is to the fourth number :
To the Rebate. 4. Subtract the Rebate from the given Sum, and tho
Remainder is the present worth. Or thus, 3. As that Sum :
Is to Tool :
To the present Payment. 4. Subtract the present payment from the given Sum,
and the remainder is the Rebate. 2. How do you prove questions in Rebate ?
A. Find the amount of the present Payment at the Time and Rate per cent given, and that will be equal to * the given Sum.
EXAMPLES. 1. What is the Rebate of 7951 11s 2d for 11 months, at 6 per cent ? Ans. 411 98 5d 3ers ft.
2. What is the present worth of 1611 10s for 19 months, at 5 per cent? Ans. 1491 138 d
3 Sold goods for 7951 11s 2d to be paid 4 months hence, what is the present worth, at 3 per cent ? Ans. 7861 78 8d.
4 What is the present worth of 40001 payable in 9 months at 45 per cent ? Ans. 38621 88 ods.
5 How much ready money for a note of 18l due 15 months hence, at 5 per cent ? Ans. 16! 188 iod.
6. Suppose 8101 were to be paid 3 months hence, allowa ing 5 per cent discount, what mæst be paid in band? Ang fool.
If a Legacy of 1000? is left me July 24, 1776, to be paid on the Christmas-day following ; what must I receive when I allow 6 per cent for present payment ? Ans. * 9751 3s id.
8. Being obliged by a bond bearing date August 29, 1776, to pay next midsummer (which is leap year) 3261 what must I pay down, if they allow me discount after the rate of 8 per cent ? Ans. 305/ 16s 6d.
9. Sold goods for 3101 to be paid at two three months (that is, half at three months, and the other half at three months after that) what must be discounted for the present payment at 5 per cent ? Ans 5l. 14s 7d.
10. Sold goods for 3001 to be paid at three two months (that is, one third at 2 months, one third-at 4 months, and one third at 6 months) what must be discounted for present payment at 4 per cent ? Ans. 31 188. 9d.
11. What is the present worth of 100l at 5 per cent payable at two four months ? Ans. 971. ils 4d.
12. I would know the present worth of 1507 payable at three four months, at 5 per cent discount ? Ans. 1451 3s 9d4.
13. What is the present worth of 2001 at 4 per cent payable as follows, viz. 1001 at two months; 501 at 3 months; and 50l at 5 months ? Ans. 1981 Os 6d.
OF EQUATION OF PAYMENTS.
THE COMMON WAY, WHAT is Equation of payments ? A. When several sums of money, to be paid at different times, are reduced to one mean time for the payment of the whole, without loss to debtor or creditor, this is called Equation of payments.
Q. Wherein may the debtor or creditor he said to suffer loss ; when the deht is paid ?
A. 1. When one mean time is assigned for the payment of the whole debt, and the money is not paid till some time afterwards; then the debtor suffers loss by laying not only ont of the principal. or sum dne, but also the interest ofihat sum for the time of forbearanee, at 3, or 4, or more per cent as they shall agree. Likewise, if the money be paid hefore it is due. then the creditor suffers loss by allowing 30 much per cent by agreement, for the time of prompt.pay Bient.
2. The loss to either party may be in redueing the seteral times of payment to one, which is not the true equated time; and then if the payment be made after the true time, the creditor suffers loss, because he receives no interest for it ; if the time agreed on be before the true time, then the debtor suffers loss, because he receives no inter est for his early payment.
Q. How is the operation wrought?
A. Multiply each payment by its time, and divide the sum of all the products by the whole debt, the quotient is the equated time.
1. A owes B 1001 whereof 501 is to be paid at 2 months, and 50l at 4 months ; but they agreed to reduce them to one payment, when must the whole be paid ? Answer, three months.
2. A merchant hath owing to him 3001 to be paid as follows ; 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 when that time must be ? Ans. 6 months.
3. F owes H 10001 whereof 2001 is to be paid present, 4001 at 5 months, and the rest at 10 months, but they agree to make one payment of the whole ; I demand the equated time ? Answer, 6 months.
4. K is indebted to L a certain sum which is to be discharged at 4 several payments, that is, i at 2 months. at 4 months, 1 at 6 months, and at 8 months ; but they agreeing to make up one payment of the whole, the
equated time is therefore demanded ? Answer, 5 months.
5. I bought of X a quantity of goods upon trust, for which H was to pay fof the deht every three months, till the whole should be discharged; but they afterwards agreed to pay the whole at one equated time ; the time is demanded? Answer, 3 months.
6. W owes Z a sum of money, which is to be paid present, 1 at 4 months, and the rest at 8 months. What is the equated time for the whole ? Answer, 3 months.
7. P owes Q 4201 which will be due 6 months hence; dut P is willing to pay him 60l now, provided he can have the rest forborne à longer time ; it is agreed on; the time of forbearance therefore is required ? An. 7 months.
Note l'his question is in Reverse Proportion See more of this Rule in Decimals,