   Chapter 13, Problem 10T ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Suppose a continuous income stream has an annual rate of flow f ( t )   = 85 e − 0.01 t , in thousands of dollars per year, and the current interest rate is 7% compounded continuously.(a) Find the total income over the next 12 years.(b) Find the present value over the next 12 years.(c) Find the capital value of the stream.

(a)

To determine

To calculate: The total income over the next 12 years if the annual rate of flow is f(t)=85e0.01t, in thousands of dollars per year, and the current rate of interest is 7% which is compounded continuously.

Explanation

Given Information:

For continuous income stream. the annual rate of flow is f(t)=85e0.01t, in thousands of dollars per year, and the current rate of interest is 7% which is compounded continuously.

Formula used:

For continuous stream, the total income for k years is 0kf(t)dt.

The exponential rule of integral is eaxdx=1aeax+C, where C is any constant.

Calculation:

Consider the function,

f(t)=85e0.01t.

Initially the value of time t is 0 and over the next 12 years, the value of t becomes 12.

The total income is,

012f(t)dt=01285e0

(b)

To determine

To calculate: The present value over the next 12 years if the annual rate of flow is f(t)=85e0.01t, in thousands of dollars per year, and the current rate of interest is 7% which is compounded continuously.

(c)

To determine

To calculate: The capital value of the stream if the annual rate of flow is f(t)=85e0.01t, in thousands of dollars per year, and the current rate of interest is 7% which is compounded continuously.

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