OPERATION. $500 given principal. 30.00=interest for 1st year. 500 530.00 am't. for 1st yr. or principal for 2d yr. Ans. $95.50.8.000=compound interest for 3 years. = 2. Find the compound interest of $300 for 4 years, at 7 Ans. per cent. 3. Find the compound interest of $125 for 3 years and 8 months, at 5 per cent. Ans. 4. Find the compound interest of $325 for 1 year, months, and 4 days, at 6 per cent. Ans. 10 5. What is the difference between the compound interest and simple interest of $1000 for 2 years and 6 months, at 6 per cent.? Ans. 6. Find the compound interest of $1525 for 8 years and 10 months, at 4 per cent. Ans. 7. What is the difference between the simple interest and compound interest of $1800 for 5 years, at 5 per cent.? Ans. 8. Find the compound interest of $275 for 3 years, months, and 10 days, at 6 per cent. OPERATION. When it is required to find the compound interest for yrs., mos., and days, it is found most convenient to find the compound in terest for the years first, and then calculate the interest for the months and days of the amount for the years, and add this interest to the compound interest for the 6 16.50 275 291.50 6 17.4900 291.50 308.9900 6 18.539400 308.99 327.529400 years; the sum will be the interest re 275 quired. 52.529400 comp. int. for 3 yr. 7.096470+ 66 4 m. & 10 dy. Ans. $59.625870 In this example we find the compound interest for 3 years; and to this add $7.096470, which is the interest on the amount $327.5294 for 3 years, for the compound interest required. We multiply by 21, half the number of months 4. $327.5294 21 6550588 545882+ Ans. $7.096470 Q. What is compound interest? Illustrate it. How do you find compound interest for years? For years, months, and days? ANNUITIES. 206. AN ANNUITY is a sum of money, payable yearly, for a certain period of years, or for ever. Pensions allowed to soldiers, &c. for public services, come under the head of annuities; so do the incomes from the rent of lands, houses, &c. When an annuity is not paid at the time it becomes due, interest is allowed upon it at the lawful rate. Annuities are calculated either at simple or compound interest. Q. What is an annuity? What kind of incomes are comprehended in annuities? When the annuity becomes due, is interest allowed? At what rate? Are annuities calculated at simple or compound interest? 207. The amount of an annuity is the sum of all the annuities remaining unpaid, with the interest on each for the time due. To find the amount of an annuity at simple interest, we calculate as in Art. 199, the interest of each annuity for the time due, and then its amount; the sum of all the amounts will be the amount required. If the annuity be at compound interest, the rule in Art. 205 will give the interest. What is the amount of an annuity of $300 for 6 years, at 6 per cent. simple interest? If the annuity had been at compound interest, we should find the amount as follows: = Ans. $2070 Q. What is meant by the amount of an annuity? How is the amount of an annuity found at simple interest? At compound interest? If the annuity run for 6 years, is the interest calculated for the whole time? Why not? When does the 6th annuity become due? If paid when due, should interest be added? EXAMPLES. 1. What is the amount of an annuity of $60 for 7 years, at 6 per cent. simple interest? Ans. 2. What is the amount of an annuity of $75 for 3 years, at 6 per cent. compound interest? Ans. 208. The present value of an annuity which is to continue for a term of years may be readily deduced from Art. 201; since to determine the present value reduces itself to find the principal, which at the given interest and time would amount to the given annuity. Thus, to find the present value of an annuity of $400, to continue 3 years at simple interest (Art. 201). Present value of $400 payable at the end of the 1st year, =$4.00% $377.35+ 1.06 Present value of $400 payable at the end of the 2d year, =$100-$357.14+ Present value of $400 payable at the end of the 3d year, =$400-$338.98+ Present value required, $1073.47+ The present value of each year's annuity being determined by dividing the annuity by the amount of $1 for the given time and rate. The sum of these results will give the present value sought. Q. How may the present value of an annuity be ascertained? To what does the question reduce itself? How is the present value of each year's annuity found? How is the required present value found? EXAMPLES. 1. What is the present value of an annuity of $60 to continue 5 years, at 6 per cent. simple interest ? Ans. 2. What is the present value of an annuity of $100, to continue 4 years, at 6 per cent. simple interest? Ans. COMMISSION AND INSURANCE. 209. COMMISSION is an allowance made to an agent for buying or selling goods, &c., or disbursing money, and is usually a certain per cent. upon the value of the articles bought or sold, or upon the money disbursed. INSURANCE is an allowance made to an individual or company for insuring property from loss by fire, shipwreck, &c., and is also a certain per cent. on the amount insured. The allowance in either case is found by multiplying the given sum by the rate per cent., and dividing the product by 100, or cutting off two figures to the right. Q. What is commission? How is it estimated? What is insurance? How is it estimated? What is the rule for finding the allowance for commission or insurance? : EXAMPLES. 1. What is the commission on $1200 at 24 per cent.? Ans. $30. 2. What would be the commission for selling $15,000 worth of flour, at 4 per cent.? Ans. $600. 3. What would be the insurance of a house, valued at $4500, for 1 year, at per cent. ? Ans. $11.25. 4. What is the insurance on $20,000, at 2 per cent.? Ans. $150. 5. What is the commission for selling 100 barrels of pork, valued at $10 per barrel, at 24 per cent.? Ans. 6. What is the commission on the sale of 100 bales of cotton, valued at $50 per bale, at 4 per cent.? Ans. |