In Problems 15-22, find the principal needed now to get each amount; that is, find the present value. 15. To get $100 after 2 years at 6% compounded monthly 332 CHAPTER 5 Exponential and Logarithmic Functions 16. To get $75 after 3 years at 8% compounded quarterly 18. To get $800 after 3 years at 7% compounded monthly 20. To get $300 after 4 years at 3% compounded daily 51 17. To get $1500 after 2- years at 1.5% compounded daily 1 oitu 22. To get $800 after 2, years at 8% compounded continuously 19. To get $750 after 2 years at 2.5% compounded quarterly 21. To get $120 after 3- years at 5% compounded continuously 4 In Problems 23-26, find the effective rate of interest. 23. For 5% compounded quarterly 24. For 6% compounded monthly 26. For 6% compounded continuously 25. For 4% compounded continuously In Problems 27-30, determine the rate that represents the better deal. 28. 9% compounded quarterly or 9-% compounded annually 30. 8% compounded semiannually or 7.9% compounded daily 27. 6% compounded quarterly or 6-% compounded annually 4. 29. 9% compounded monthly or 8.8% compounded daily 31. What rate of interest compounded annually is required to double an investment in 3 years? 32. What rate of interest compounded annually is required to double an investment in 6 years? 34. What rate of interest compounded annually is required to triple an investment in 10 years? 36. (a) How long does it take for an investment to triple in vol if it is invested at 6% compounded monthly? (b) How long does it take if the interest is compounded continuously? 33. What rate of interest compounded annually is required to triple an investment in 5 years? 35. (a) How long does it take for an investment to double in value if it is invested at 8% compounded monthly? (b) How long does it take if the interest is compounded continuously? 37. What rate of interest compounded quarterly will yield an effective interest rate of 7%? 38. What rate of interest compounded continuously will yield an effective interest rate of 6%? nd (h) Applications and Extensions rib 22922A 39. Time Required to Reach a Goal If Tanisha has $100 to invest at 4% per annum compounded monthly, how long will it be before she has $150? If the compounding is continuous, how long will it be? 40. Time Required to Reach a Goal If Angela has $100 to invest at 2.5% per annum compounded monthly, how long will it be before she has $175? If the compounding is continuous, how long will it be? 41. Time Required to Reach a Goal How many years will it take for an initial investment of $10,000 to grow to $25,000? 46. Paying off a Loan John requires $3000 in 6 months to pay off a loan that has no prepayment privileges. If he has the $3000 now, how much of it should he save in an account paying 3% compounded monthly so that in 6 months he will have exactly $3000? 47. Return on a Stock George contemplates the purchase of 100 shares of a stock selling for $15 per share. The stock pays no dividends. The history of the stock indicates that it should grow at an annual rate of 15% per year How much should the 100 shares of stock be worth