University:
Cornell University
Course:
NBA 4120 | Equity Investment Research and Analysis
Academic year:

2024
Views:

366

Pages:

2
Author:

larbiwxcvbn

Review of Exponents [Day 6] From Day 5! FACTOR [Answers on Day 5 WS] 19. x²y³ - x⁴y² x²y²(y - x²) 20. x⁵y² - x³y⁷ x³y²(x² - y⁵) 21. x^(3/2)y^(-1/2) - x^(1/2)y^(1/2) x^(1/2)y^(-1/2)(x - y) 22. x^(1/2)y^(-1/2) - x^(3/2)y^(1/2) x^(1/2)y^(-1/2)(1 - xy) 23. (x-1)^(1/2) - x(x-1)^(-1/2) (x-1)^(-1/2)[(x-1)^1 - x] (x-1)^(-1/2)(-1) = -(x-1)^(-1/2) 24. (x+1)^(3/2) - 4(x+1)^(1/2) (x+1)^(1/2)[(x+1)^1 - 4] (x+1)^(1/2)(x-3) 25. (x²+1)^(3/2) - x²(x²+1)^(1/2) (x²+1)^(1/2)[(x²+1)^1 - x²] (x²+1)^(1/2)(1) = (x²+1)^(1/2) 26. (x²+2)^(1/2) - x²(x²+2)^(-1/2) (x²+2)^(-1/2)[(x²+2)^1 - x²] (x²+2)^(-1/2)(2) = 2(x²+2)^(-1/2) New Notes [Day 6] Use a calculator to evaluate. 1. e^(0.08) = 1.0833 2. e² = 7.3891 3. e^(-4) = 0.0183 4. e^(√2) = 4.1133 5. e = 2.7182 6. Suppose you invest $500 at 6% annual interest. Calculate the amount you would have after one year if the interest is compounded as follows: a. quarterly 1 Define: Effective Annual Yield = (new - original) / original 10. Find the effective annual yield for each answer in #9. a. (530.68-500)/500 = 6.136% b. (530.84-500)/500 = 6.168% c. (530.92-500)/500 = 6.184% d. (530.92-500)/500 = 6.184% 11. One hundred dollars deposited in a bank that compounds interest quarterly yields $107.50 over 1 year. a. Find the annual interest rate 107.50 = 100(1+r/4)^(4*1) 1.075 = (1+r/4)^4 (1.075)^(1/4) = 1 + r/4 r/4 = (1.075)^(1/4) - 1 r = 4[(1.075)^(1/4) - 1] = 7.307% b. Find the effective annual yield (107.50-100)/100 = 7.5% 12. After a year during which interest is compounded quarterly, an investment of $800 is worth $851. What is the effective annual yield? (851-800)/800 = 6.375% 13. With which plan would an investor earn more, Plan A or Plan B? Plan A Plan A: A 6.5% annual rate compounded annually over a 10-year period (1+0.065)^10 = 1.7908 Plan B: A 5.5% annual rate compounded quarterly over a 10-year period (1+0.055/4)^(4*10) = 1.6436 14. With which plan would an investor earn more, Plan A or Plan B? Plan A Plan A: A 8% annual rate compounded quarterly over a 5-year period (1+0.08/4)^(4*5) = 1.4859 Plan B: A 7.5% annual rate compounded daily over a 5-year period (1+0.075/365)^(365*5) = 1.4549 15. Suppose that $1000 is invested at 7% interest compounded continuously. How much money would be in the bank after 5 years? 1000e^(0.07*5) = $1419.07 Define: Rule of 72 72/r if investment is compounded annually 72/(r*n) if investment is compounded n times per year 16. Suppose $1000 is invested at 8% interest compounded annually. How long would it take for the investment to double? 72/8 = 9 years 17. Suppose $2050 is invested at 6% interest compounded monthly. How long would it take for the investment to double? 72/(6/12) = 12 years 18. Suppose that $3200 is invested at 2.5% interest compounded monthly. How long would it take for the investment to double? 72/(2.5/12) = 34.56 years

Invest Review of Exponents Day 6 Solution Key

Related Documents

Recommended Documents

Description

Related Documents

Free up your schedule!

Take 5 seconds to unlock