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2. Divide the given sum by the amount of $1, or £1, at the given rate and time, the quotient will be the present worth. Subtract the present worth from the given sum, and the remainder is the discount.*
1. What is the present worth of $132,50, due 1 year hence, at 6 per cent discount ? [By Rule 1.]
[By Rule 2.)
The amount of $1 for 1 As 106 : 6 :: 132,50
year, at 6 per cent, is $1,06.
530 Ans. 125,00 present worth.
2. What sum, in ready money, will discharge a debt of £540, due 3 years 4 months hence, at 6 per cent ? Am't of £1 for 3 years 4
£ £ £ months, at 6 per cent, S 1,20)540,00(450 Ans. 3. What is the present worth of 500 dollars due 2 years 6 months hence, at 5 per cent ?
). 4. What is the present worth of $1080, due 5 years 10 months hence, at 6 per cent ?
Ans. $800. 5. What is the discount of $460, due 2 years 6 months hence, at 6 per cent?
Ans. $60. 6. Bought goods to the amount of $1260,50 on eight months credit : how much ready money must I pay to discharge the same, discounting at 6 per cent ?
Ans. $1212, lc. 9m. + Note. When sundry sums are payable at different times, find the present worth of each payment separately, and then add them together.
* This is precisely the same as Case II, Simple Interest by Decimals, since the present worth of any sum is such a principal as, if put at interest for the given rate and time, would amount to said sum, it follows that we have the amount, time and rate per cent given, to find the principal, or present worth.
7. What is the present worth of $1000, one-half payable in 8 months, and the other half payable in 8 months after that, at 6 per cent discount ? Ans. $943, 73c. 2m. +
8. What is the discount of $1384, of which $500 are payable in 1 year 4 months, and the remainder at the end of 4 years, at 6 per cent ? Ans. $208, 13c. 3m. +
EQUATION OF PAYMENTS.
Equation of Payments is the method of finding the mean time to pay at once several debts, due at different times.
Multiply each payment by the time at which it is due, then divide the sum of the products by the sum of the payments, and the quotient will be the answer.
1. A owes B $380, to be paid $100 in 6 months, $120 in 7 months, and $160 in 10 months ; what is the equated time for the payment of the whole debt
100 x 6= 600
$380)3040(8 months. Ans. 2. A merchant owes $500, payable as follows; $150 in 4 months ; $200 in 6 months, and the rest at 8 months, and he is to make one payment of the whole ; I demand the equated lime.
Ans. 6 months. 3. A owes B $150, to be paid in 6 months ; $180 to be paid in 8 months ; $200 to be paid in 10 months, and $250 to be paid in 12 months ; what is the equated time for the payment of the whole ?
Ans. 9.16 months. 4. What is the equated time for the payment of $1200 of which $500 are payable in 10 months, $400 in 20 months, and the rest in 2) years ?
Ans. 18} months. 5. A merchant owes $1800, to be paid } in 5 months, in 10 months, j in 18 months, and the rest in 20 months,
andwishes to pay the whole at once; I demand the equated time.
Ans. 13 months.
Questions. 1. What is Discount?
5. When several sums are payable at 2. What is the present worth of any different times, how do you find the presum ?
sent worth? 3. (Rules.) How do you find the Discount of any sum?
1. What is Equation of Payments ? 4. How do you find the present 2. What is the rule for Equation of worth?
ANNUITIES AT SIMPLE INTEREST. An annuity is a sum of money payable every year, or for a certain number of years, or forever.
When the annuity is not paid at the time it becomes due, it is said to be in arrears.
The sum of all the annuities, together with the interest due on each for the time they have been forborne, is called the amount.
1. To find the amount of an Annuity.
1. Cast the interest on the given annuity for one year, then for two years, three years, four years, &c., up to the given time, less 1. Then multiply the annuity by the given number of years, and add the product to the whole interest, and the sum will be the amount required.
1. If an annuity of 200 dollars per annum remain unpaid, (that is, in arrears,) 6 years, what is the amount due, reckoning interest at 6 per cent. ? The interest of $200 for 1 year is
$12,00 2 years is
24,00 3 years is
36,00 4 years is
48,00 5 years is
60,00 6 years annuity at $200 per year is
1200,00 Ans. $1380,00
2. If a salary of $325 per year remain unpaid, or in arrears, for the term of 5 years, what amount is then due, interest at 6 per cent ?
Ans. $1820. 3. If a man, having an annual pension of $75 a year, receive no part of it until the end of 7 years, what is the amount due, interest at 5 per cent ?
Ans. $603,75. 2. When an annuity is bought off, or paid all at once, at the beginning of the first year, the sum that is paid for it is called the present worth. To find the present worth of an annuity at Simple Interest:
Find the present worth of each year by itself, discounting from the time it falls due, and the sum of all the present worths will be the present worth required.
i. What is the present worth of an annuity of $500, to continue 4 years, at 6 per cent per annum ? As 106 : 100 :: $500 : $471,6981+pres. worth 1st year.
112 : 100 :: 500 : 446,4285+
423,7288+ 124 : 100 :: 500 : 403,2258+
2d year. 3d year: 4th year.
$1745,0812=$1745, 8cts. 13 m. 2. What sum of ready money is equal to an annuity of 100 dollars to continue 3 years, discounting at 6 per cerit?
Ans. $268,371. 3. What is 600 dollars yearly rent, to continue 4
years, worth in ready money at 6 per cent ? Ans. $2094, 091c.
4. What is the present worth of an annual salary of 800 dollars, to continue 5 years, at 6 per cent ?
Ans. $3407 51,2c.
Questions. 1. What is an annuity ?
4. How do you find the amount of an 2. When is an annuity said to be in ar- annuity ? rears?
5. What is the present worth of an 3. What is the sum of all the annui- annuity ? ties, together with their interest; call 6. How do you find the present wortb ed?
of an annuity ?
TO FIND THE NET WEIGHT OF ANY GOODS OR MER
CHANDIZE, WHERE TARE IS ALLOWED. This is a part of the rule formerly called Tare and Tret, the remainder of which is now become obsolete in the United States, there being no such allowances as Tret, Cloff, &c. now made use of. We shall here notice,
1. Gross weight, which is the whole weight of any kind of goods, including the box, cask, bag, &c. that contains them.
2. Tare, which is an allowance made for the box, cask, bag, &c., which contains them, and is either at so much per box, bag, &c., or at so much per cwt., or at so much on ihe whole gross weight.
3. Net, which is what remains after the Tare is taken out.
If the question be an Invoice, add all the gross weights into one sum, and all the tares into another sum ; then subtract the whole tare from the whole gross, the remainder will be the net.
EXAMPLES. 1. What is the net weight of 4 hogsheads of sugar marked with the gross weights and tares, as follows ?
14 Tare 105 No. 2, 8 3 20
87 9 1 17
95 No. 4. 8 2 13
36 Whole tare 3711b.=3
Ans. 33 1 1 net. 2. What is the net-weight of 5 tierces of rice, No. and weight as follows?
4 3 15 Tare 41