257. Hence, to calculate compound interest. Cast the interest on the given principal for 1 year, or the specified time, and add it to the principal; then cast the interest on this amount for the next year, or specified time, and add it to the principal as before. Proceed in this manner with each successive year of the proposed time. Finally, subtract the given principal from the last amount, and the remainder will be the compound interest. 2. What is the compound interest of $350 for 4 years, at 6 per cent. ? 3. What is the compound interest of $865 for 5 years, at 7 per cent.? 4. What is the amount of $250 for 6 years, at 5 per cent. compound interest? 5. What is the amount of $1000 for 3 years, at 4 per cent. compound interest, payable semi-annually? years, at 5 per 6. What is the amount of $1200 for 2 years, at 6 per cent. compound interest, payable quarterly? 7. What is the amount of $800 for 3 cent. compound interest, payable semi-annually? 8. What is the amount of $1500 for 5 years, at 7 cent. compound interest? per 9. What is the amount of $2000 for 2 years, at 3 per cent. compound interest, payable quarterly? 10. What is the amount of $3500 for 6 years, cent. compound interest? at 6 per Note. This and the next two examples may be solved either by the rule, or by the Table below. 11. What is the amount of $1860 for 8 years, at 7 per cent. compound interest? 12. What is the amount of $20000 for 10 years, at 3 per cent. compound interest? QUEST.-257. How is compound interest calculated? TABLE, Showing the amount of $1, or £1, at 3, 4, 5, 6, and 7 per cent., compound interest, for any number of years, from 1 to 35. Yrs. | 3 per cent. | 4 per cent. | 5 per cent. | 6 per cent. | 7 per cent. 258. To calculate compound interest by the preced ing table. Find the amount of $1, or £1 for the given number of years by the table, multiply it by the given principal, and the product will be the amount required. Subtract the principal from the amount thus found, and the remainder will be the compound interest. 13. What is the compound interest of $200 for 10 years, at 6 per cent.? What is the amount ? Operation. $1.790848 Amt. of $1 for 10 years by table. $358.169600 amount required. Ans. $158.1696 interest required. 14. What is the amount of $350 for 12 years, at 4 per cent.? 15. What is the amount of $469 for 15 years, at 3 per cent.? What the interest? 16. What is the interest of $500 for 24 years, at 6 per cent. ? 17. What is the interest of $650 for 30 years, at 7 per cent. ? DISCOUNT. 259. DISCOUNT is the abatement or deduction made for the payment of money before it is duc. For example, if I owe a man $100, payable in one year without interest, the present worth of the note is less than $100; for, if $100 were put at interest for 1 year, at 6 per cent., it would amount to $106; at 7 per cent., to $107; &c. sideration, therefore, of the present payment of the note, jus tice requires that he should make some abatement from it. This abatement is called Discount. In con QUEST.-258. How is compound interest computed by the Table? 259. What is discount? What is the present worth of a debt, payable at some future time, without interest? The present worth of a debt payable at some future time without interest, is that sum which, being put at legal interest, will amount to the debt, at the time it becomes due. Ex. 1. What is the present worth of $545, payable in 1 year and 6 months without interest, when money is worth 6 per cent. per annum? Analysis. The amount, we have seen, is the sum of the principal and interest. (Art. 234.) Now the amount of $1 for 1 year and 6 months, at 6 per cent., is $1.09; (Art. 237;) that is, the amount is 108 of the principal $1. The question then resolves itself into this: $545 is 108 of what principal? If $545 is 108, 10 is 545÷109, or $5; and 100-$5×100, which is $500. Or, we may reason thus: Since $1.09 (amount) requires $1 principal for the given time, $545 (amount) will require as many dollars as $1.09 is contained times in $545; and $545+$1.09-$500. That is, the present worth of $545, payable in 1 year and 6 months, is $500, which is the answer required. PROOF.-$500×.09 $45, the interest for 1 year and 6 months; and $500+$45-$545 the given amount. (Art. 247.) Hence, 260. To find the present worth of any sum, payable at a future time without interest. First find the amount of $1 for the time, at the given rate, as in simple interest; (Art. 247;) then divide the given sum by this amount, and the quotient will be the present worth. The present worth subtracted from the debt, will give the true discount. OBS. This process is often classed among the Problems of Interest, in which the amount, (which answers to the given sum or debt,) the rate per cent., and the time are given, to find the principal, which answers to the present worth. QUEST.-260. How do you find the present worth of a debt? How find the discount? 2. What is the present worth of $250.38, payable in 8 months, when money is worth 6 per cent. per annum? What is the discount? 3. What is the present worth of $475, payable in 1 year, when money is worth 7 per cent. per annum? 4. What is the present worth of $175, payable in 2 years, when money is worth 7 per cent. per annum? 5. What is the present worth of $1000, payable in 4 months, when the rate of interest is 6 per cent. ? 6. What is the discount on $750, due 6 months hence, when interest is 5 per cent. per annum? 7. A man sold a farm for $1800, payable in 15 months: what is the present worth of the debt, allowing the rate to be 6 per cent. ? 8. I have a note of $1150.33, payable in 9 months: what is its present worth at 7 per cent. interest per annum? 9. A merchant sold goods amounting to $840.75, payable in 6 months: how much discount should he make for cash down, when money is worth 7 per cent.? 10. What is the discount on a draft of $2500, payable in 3 months, at 4 per cent. per annum? 11. What is the present worth of $5000, payable in 2 months, at 6 per cent. per annum.? 12. What is the difference between the discount on $500 for 1 year, and the interest of $500 for 1 year, at 6 per cent.? |