Explanation Formula used: The sum of first n terms of a geometric series with common ratio r is given by S n = a 1 ( 1 − r n ) 1 − r , where a 1 is the first term of the series. Method used: Present Value of an Income Stream: The present value of an income stream of R ( t ) dollars per year, earning interest at the rate of r per year compounded continuously, is given by P V = ∫ 0 T R ( t ) e − r T d t . Calculation: It is given that the annual income of Sam Simpson’s children from the trust fund is $10000 and interest rate of the fund compounded continuously is 6% per year. That is, r = 6 % that is r = 0.06 , R ( t ) = 10000 . Substitute r = 0.06 , R ( t ) = 10000 , T = 1 in P V = ∫ 0 T R ( t ) e − r T d t and obtain the present value of the income in the first year as follows. ∫ 0 T R ( t ) e − r T d t = ∫ 0 1 10000 e − ( 0.06 ) ( 1 ) d t = 10000 e − ( 0.06 ) ( 1 ) [ t ] 0 1 = 10000 e − ( 0.06 ) Thus, the present value of the income in the first year is 10000 e − ( 0.06 ) . Similarly, the present value of the income in the second year is 10000 e − ( 0.06 ) ( 2 ) , third year is 10000 e − ( 0.06 ) ( 3 ) and so on. On continuing, the present value of the income of the n th year is e − ( 0.06 ) ( n ) . Therefore, the amount of trust fund is the sum of the income over the life time of the children

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ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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Chapter 11, Problem 48RE

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The amount of money required to place in the trust so that the fund will earn an interest rate of 6% per year.

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Chapter 11, Problem 47RE

Chapter 11, Problem 49RE

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Chapter 11 Solutions

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Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - In Exercises 1120, find the nth Taylor polynomial...Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Let f(x) = ex. a. 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The amount of money required to place in the trust so that the fund will earn an interest rate of 6% per year.

Solution Summary: The author calculates the present value of an income stream of R ( t ) dollars per year, earning interest at the rate of r per. year compounded continuously.

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The amount of money required to place in the trust so that the fund will earn an interest rate of 6% per year.

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Chapter 11 Solutions