Explanation Given: The future value is S = $ 150 , 000 and the interest rate is 6%. The annuity is compounded annually for 11 years. Formula used: The periodic payment is R = S i ( 1 + i ) n − 1 . Where, S is the future value; R is the periodic payment; i is the interest rate per period n is the number of periods. Calculation: Given that, the future value is S = $ 150 , 000 . Since the fund is compounded semiannually, the number of payments made in a year is m = 2 . It is given that the annuity is for t = 11 years . Hence, the number of periods is n = m t . That is, 11 × 2 = 22 . It is given that the interest rate is r = 6 % . Then the interest rate per period is, i = r m = 6 % 2 = 0.06 2 = 0

Finite Mathematics and Calculus with Applications

1st Edition

ISBN: 9781323188361

Author: Margaret Lial

Publisher: Pearson Education

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Chapter 5.2, Problem 32E

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Chapter 5.2, Problem 31E

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There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three investment? STEP 1: The formula for compound interest is A = nt = P(1 + − − ) n², where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to A = Pert Find r and n for each model, and use these values to write A in terms of t for each case. Annual Model r=0.10 A = Y(t) = 1150 (1.10)* n = 1 Quarterly Model r = 0.10 n = 4 A = Q(t) = 1150(1.025) 4t Continuous Model r=0.10 A = C(t) =…

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Finite Mathematics and Calculus with Applications

Ch. 5.1 - Find the maturity value for a 3000 loan at 5.8%...Ch. 5.1 - Prob. 2YT Ch. 5.1 - Prob. 3YT Ch. 5.1 - Prob. 4YT Ch. 5.1 - Prob. 5YT Ch. 5.1 - Prob. 6YT Ch. 5.1 - Prob. 7YT Ch. 5.1 - Prob. 8YT Ch. 5.1 - Prob. 1WE Ch. 5.1 - Prob. 2WE

Ch. 5.1 - Prob. 3WE Ch. 5.1 - Prob. 4WE Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - What is the difference between t and n?Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Find the present value (the amount that should be...Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - For each of the following amounts at the given...Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.1 - Prob. 59E Ch. 5.1 - Prob. 60E Ch. 5.1 - Prob. 61E Ch. 5.1 - Prob. 62E Ch. 5.1 - Prob. 63E Ch. 5.1 - Prob. 64E Ch. 5.1 - Savings On January 1, 2010, Jack deposited 1000...Ch. 5.1 - Savings Eric deposits 100 into a savings account...Ch. 5.1 - Interest Bruce and Robbie each open new bank...Ch. 5.1 - Prob. 68E Ch. 5.1 - Effective Rate In 2014, the Home Savings Bank paid...Ch. 5.1 - Prob. 70E Ch. 5.1 - Prob. 71E Ch. 5.1 - Prob. 72E Ch. 5.1 - Prob. 73E Ch. 5.1 - Prob. 74E Ch. 5.1 - Prob. 75E Ch. 5.1 - Prob. 76E Ch. 5.1 - Prob. 77E Ch. 5.1 - Prob. 78E Ch. 5.1 - Prob. 79E Ch. 5.1 - Prob. 80E Ch. 5.2 - Prob. 1YT Ch. 5.2 - Prob. 2YT Ch. 5.2 - Prob. 3YT Ch. 5.2 - Prob. 4YT Ch. 5.2 - Prob. 1WE Ch. 5.2 - Prob. 2WE Ch. 5.2 - Prob. 1E Ch. 5.2 - Prob. 2E Ch. 5.2 - Prob. 3E Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - Prob. 6E Ch. 5.2 - Prob. 7E Ch. 5.2 - Prob. 8E Ch. 5.2 - Prob. 9E Ch. 5.2 - Prob. 10E Ch. 5.2 - Prob. 11E Ch. 5.2 - Prob. 12E Ch. 5.2 - Prob. 13E Ch. 5.2 - Prob. 14E Ch. 5.2 - Explain how a geometric sequence is related to an...Ch. 5.2 - Prob. 16E Ch. 5.2 - Prob. 17E Ch. 5.2 - Prob. 18E Ch. 5.2 - Prob. 19E Ch. 5.2 - Prob. 20E Ch. 5.2 - Find the future value of each ordinary annuity, if...Ch. 5.2 - Prob. 22E Ch. 5.2 - Prob. 23E Ch. 5.2 - Prob. 24E Ch. 5.2 - Prob. 25E Ch. 5.2 - Prob. 26E Ch. 5.2 - Prob. 27E Ch. 5.2 - Prob. 28E Ch. 5.2 - Prob. 31E Ch. 5.2 - Prob. 32E Ch. 5.2 - Prob. 33E Ch. 5.2 - Prob. 34E Ch. 5.2 - Prob. 35E Ch. 5.2 - Prob. 36E Ch. 5.2 - Prob. 37E Ch. 5.2 - Prob. 38E Ch. 5.2 - Prob. 39E Ch. 5.2 - Prob. 40E Ch. 5.2 - Prob. 41E Ch. 5.2 - Prob. 42E Ch. 5.2 - Prob. 43E Ch. 5.2 - Prob. 44E Ch. 5.2 - Prob. 45E Ch. 5.2 - Prob. 46E Ch. 5.2 - Business and Economics 47. 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The period payment to be made into a sinking fund.

Solution Summary: The author explains that the annuity is compounded annually for 11 years and the future value is S=150,000. Substitute cR=

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Chapter 5 Solutions