RULE FOR COMPOUND INTEREST. Find the amount of the given principal (Art. 222) for the 1st yr., and make it the principal for the 2d yr. Find the amount of this principal for the 2d yr., make it the principal for the 3d yr., and so on, for the given number of yr. From the last amount subtract the given principal; the remainder will be the compound interest. NOTES.-1. When the interest is payable half-yearly, or quarteryearly, find the Int. for a half, or a quarter year, and proceed in other respects as when the Int. is payable yearly. 2. When the time is years, months, and days, find the amount for the years, then compute the Int. on this for the months and days, and add it to the last amount Find the Amount, at 6 %, Compound Interest, 7. Ans. $25.101+ $200 for 2 yr., at 6 %, payable semi-annually. 8. Find the amount of $500 for 2 yrs., at 20% compound interest, payable quarterly. 9. What is the compound interest mon., at 6 %? 10. What the compound interest of mon. 15 da., at 6% ? Ans. $738.727+ of $300 for 2 yr. 6 Ans. $47.192+ $1000 for 2 yr. 8 Ans. $171.353 ART. 234. Since the amount of $2, for any given time, will be twice the amount of $1; the amount of $3, three times as much, &c.; Therefore, If a table be formed containing the amounts of $1 for 1, 2, 3, &c., years, any of these amounts multiplied by a given Principal will give its amount at Compound Interest for the same time and rate. See Table, page 238. TABLE Showing the amount of $1, at 3, 4, 5, 6, 7 and 8 per cent., Com pound Interest, for any number of years, from 1 to 25. 22 3.399564 4.140562 5.033833 3.603537 4.430401 5.436540 4.740529 21 1.860295 2.278768 2.785963 5.871463 5.072366 6.341180 5.427432 6.848475 11. What, by the Table, will be the Amount of $70 for 9 yr., at 5% compound interest? SOLUTION.-By the Table, the amount of $1 for 9 yrs., at 5 pr. ct. is $1.551328; and $1.551328X70=$108.59296 12. Of $345 for 10 yr., at 6 %? Ans. $617.84+ EXPLANATION.-Take any two periods whose sum is 41 years, thus, 20yr.-21 yr.=41 yr., and find the amount for the 1st period: then regard this a new principal, and find its amount for the 2d period the last amount will be the Ans. The Tabular number for 20 yr. is 3.207135; this, multiplied by 200, gives $641.427, amount for 20 yr.: Tabular number for 21 yr. is 3.399564, which×641.427 $2180.572+ Ans. What, by the Table, will be the Interest 14. Of $890 for 30 yr., at 6 %? 15. Ans. $4221.70+ $200 for 70 yr., at 5 % ? Ans. $5885.28+ ART. 235. DISCOUNT Is a deduction made for the payment of money before it is due. For example, If a debt of $106, due one year hence without interest, be paid at the present time, the sum paid, with one year's interest added, should make $106. And, If the rate per cent. is 6, this sum would be $100; for, the amount of $100 at interest for 1 year, at 6%, is $106. Art. 220. The PRESENT WORTH of a debt payable at a future time without interest, is that sum which, at a specified rate % for the same time, would amount to the debt. The DISCOUNT is the sum deducted for present payment. ART. 236. 1. Find the Present Worth of $224, due 2 yr. hence, without interest, money being worth 6 % per annum. SOLUTION. The amount of $1 for 2 years, at 6 per cent., is $1.12; hence, the present worth of each $1.12 of the given sum, is $1. And, the present worth of $224, will be as many times $1, as $1.12 is contained times in $224. $224.$1.12 200. Ans. $200. = PROOF. The amount of $200 for 2 years, at 6 per cent., is $224. Art. 220. *2. Find the present worth of $81, due 2 yr. hence, no Int., money worth 4 % per annum. Ans. $75. REVIEW. 234. What does the Table show? By means of it, how find the amount of any sum at compound interest? 235. What is disccunt? What the present worth of a debt, payable at a future time without interest? The discount? OF PRESENT WORTH. To find the present worth of a sum payable at a future time without interest: Rule.-Divide the given DEBT by the amount of one dollar for the given time, at the given rate per cent.; the quotient will be the PRESENT WORTH, To find the DISCOUNT, subtract the PRESENT WORTH from the DEBT. Or, by PROPORTION. As the amount of any principal, (as $1, or $100,) for the given time, at the given rate per cent., is to the principal, so is the given debt to the present worth. NOTE. In the following Examples, the rate per cent. is 6, unless some other is given; and when the present worth of any sum is required, it is supposed not to be at interest. What is the Present Worth of ANSWERS. 7. $675.00 due 5 yr. 10 mon. hence? $500. $300. 9. $493.20 due in 7 yr. 9mon. 20 da.? $335.89+ $276.64 due 2 years hence?. $29.64 12. $330.00 due 3 yr. 4 mon. hence? 13. Bought $260 worth of goods, on what sum will pay the debt now? 14. If money is worth 12 %, what is the present worth of $235.20, duc 1 year hence? 15. What is the discount, at 7%, of year hence? Ans. $210. $401.25, due 1 Ans. $26.25 $55.00 8 mon. credit: Ans. $250. 16. What is the difference between the simple Int. and discount of $1080 for 10 yr., at 6 %? Ans. $243. 17. A man was offered $1122 for a house, in cash, or $1221, payable in 10 mon. without Int. He chose the latter how much did he lose, supposing the note discounted at the rate of 12 % per annum ? ART. 237. Ans. $12. PAYMENTS AT DIFFERENT TIMES. When payments without interest, are to be made at different times, to find the present value of the whole, Find the present worth of each payment, and take their sum. 18. Find the present value of a debt of $956.34, onethird to be paid in 1 yr., one-third in 2 yr., and one-third in 3 yr.; money being worth 5 %. Ans. $870.60 19. Of a debt of $1440, of which one-half is payable in 3 mon., one-third in 6mon., and the remainder in 9 mon.; Int. at 6 % per annum. Ans. $1405.044+ 20. Of a debt of $700, of which $60 are to be paid in 6 mon., $180 in 1yr., $260 in 18mon., the remainder in 2 yr.; Int. 6 % per annum. Ans. $645.167+ DISCOUNT AND INTEREST COMPARED. ART. 238. A comparison of Discount with Interest (Art. 219), shows that the Present Worth corresponds to the principal, the debt to the amount, and the discount to the interest of the principal for the given time, at the given rate per cent.; hence, When the time, rate per cent., and amount are given, the principal is found (Art. 236) by dividing the amount by the amount of $1 for the given time, at the given rate per cent. To find the interest, subtract the principal from the amount. 1. The amount is $650; time, 5 yr.; rate, 6 % what is the principal? Ans. $500. : REVIEW.-236. How find the present worth, Rule? The discount? How, by proportion? 237. When payments without interest are to be made at different times, how find the present value of the whole? |