2.2 Compound Interest and the Number el 2. If $6,000 is invested in an account paying 6.5% interest. how much will it gr

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2 2 Compound Interest And The Number El 2 If 6 000 Is Invested In An Account Paying 6 5 Interest How Much Will It Gr 1 (72.45 KiB) Viewed 41 times

2.2 Compound Interest and the Number el 2. If $6,000 is invested in an account paying 6.5% interest. how much will it grow to in 7 years if the interest is com- pounded (a) quarterly? (b) 24 times per year? (c) continuously? 3. If $100 is invested in an account paying 7% interest, how much will it grow to in 20 years if the interest is com- pounded (a) 365 times a year? (b) continuously? 4. Suppose that on the day when his granddaughter is born, a man invests $5,000 in her name in an account paying 4.5% interest. How much will there be on her 21st birthday if the interest is compounded (a) annually? (b) quarterly? (c) continuously? 5. Which of the following will provide a greater return af- ter one year on an initial investment: a 6% interest rate compounded four times a year, or a 4% interest rate com pounded six times a year? 6. Which of the following will provide a greater return on an initial investment at an annual interest rate of 5%: com- pounded 12 times a year for 1 year, or compounded six times a year for 2 years? 7. Suppose you put $1,000 in an account paying 7.5% inter- est, compounded continuously. How much will there be at the end of (a) 6 months? (b) 8 months? (c) 27 months? 8. Suppose you make an initial deposit in an account paying 6.25% interest, compounded continuously. By what fac- tor does your investment increase (a) after 6 months (b) after 1 year (c) after of 18 months? 9. Suppose you put $10,000 in an account paying 4.5% in- terest, compounded continuously. How much will there be at the end of (a) 6 months? (b) 18 months? (c) 36 months? 10. Suppose that you open an account paying 5% interest. compounded continuously. How much should you de- posit to ensure that there will be $10,000 in 7 years? 11. Suppose that you open an account paying 12% interest, compounded continuously. How much should you de- posit to ensure that there will be $2.000 in 6 months? 12. Suppose that you open an account paying 7% interest. compounded annually. How much should you deposit to ensure that there will be $5,000 in 10 years? In Exercises 13-21, find the given limit. First express your answer as an exponential expression without using a cal- culator, then use a calculator to evaluate it to four decimal places 13. lim 20 15. lim 17. lim BAN 19. lim 101 10 (1-1) 21. lim 1000 (1+ 22. Make a table of values choices of n: 10, 50, your calculator to find do you explain it? 14. lim (1+1) 14 == 0(1-2)* 16. lim 100 18. Tim (1+1) 2 20. lim (1+)* 442 135 of (1+1/(2n)) for the following 100, 500, 1,000, 5,000. Next, use e. What do you observe, and how 23. Make a table of values of (1-1/n) for the following choices of m: 10, 50, 100, 500, 1,000, 5,000. Next, use your calculator to find 1/e. What do you observe, and how do you explain it? 24. Make two tables: the first for (1+1/(5))" and the second for (1+1/n), both for n from 1,000 to 10,000 in steps of 1,000. What do you observe when you compare the tables? How do you explain it? 25. Make a table of values of (1+3/n)-2 form from 1,000 to 10,000 in steps of 1,000. Toward what limit are these numbers tending? In Exercises 26-28, treat each month as if it were exactly 1/12 of a year 26. Suppose that on the first of next month you deposit $3,000 in an account paying 4.5% annual interest, compounded monthly. Make a table of the balance in the account at the end of each of the next 48 months. 27. Suppose that on the first of every month you deposit $100 in an account paying 3.6% annual interest, compounded monthly. Assuming that you never make any withdrawals make a table of the balance in the account immediately af- ter your monthly deposit for each of the first 36 months 28. A retired person has $120,000 in an account that pays 5% annual interest, compounded continuously. She never adds to the balance and on the first day of each month she withdraws $300. Make a table of the balance in the account immediately after her withdrawal for each of the next 36 months. 29. Solve the equation et 30. Solve the equation e' = 2-t.