Explanation Given: An investor has $10,000 to invest in either a bond that matures in 5 years or a business that will produce a continuous stream of income over next 5 year with rate of flow f ( t ) = 2 , 250 . Both the bond and the continuous income stream earn 3.75%, compounded continuously. Definition used: If f ( t ) is the rate of flow of a continuous income stream 0 ≤ t ≤ T , and if the income is continuously invested at a rate r , compounded continuously, then the future value F V at the end of T years is given by, F V = ∫ 0 T f ( t ) e r ( T − t ) d t = e r T ∫ 0 T f ( t ) e − r t d t Calculation: The future value of investment of $10,000 in bond is calculated as follows. The money invested in bond is worth 3.75% compounded continuously, and then future value of a $10,000 investment in 5 years is, A = 10 , 000 e 0.0375 × 5 = 10 , 000 ( 1.2062 ) ≈ $ 12 , 062 The future value of $10,000 in bond investment at 3.75% compounded continuously at the end of 5 years is $12,062. Similarly, the future value of the business at 3.75% interest, compounded continuously for 5 years, of the continuous income stream with rate of flow f ( t ) = 2 , 250 is calculated as follows. Substitute T = 5 , f ( t ) = 2 , 250 , and r = 0

Calculus for Business Economics Life Sciences and Social Sciences Plus NEW

13th Edition

ISBN: 9780321925138

Author: Raymond Barnett

Publisher: PEARSON

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Chapter 6.2, Problem 50E

To determine

To compare: The future values of these investments to determine which the better choice is over the next 5 years.

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Chapter 6.2, Problem 49E

Chapter 6.2, Problem 51E

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Calculus for Business Economics Life Sciences and Social Sciences Plus NEW

Ch. 6.1 - Matched Problem 1 Find the area bounded by f(x) =...Ch. 6.1 - Matched Problem 2 Find the area between the graph...Ch. 6.1 - Prob. 3MP Ch. 6.1 - Matched Problem 4Find the area bounded by f(x) =6 ...Ch. 6.1 - Matched Problem 5Find the area bounded by f(x)=2x2...Ch. 6.1 - Matched Problem 6Find the area (to three decimal...Ch. 6.1 - Prob. 7MP Ch. 6.1 - Prob. 1ED Ch. 6.1 - In Problems 18, use geometric formulas to find the...Ch. 6.1 - In Problems 18, use geometric formulas to find the...

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