Chapter 14, Problem 25RE

### Mathematical Applications for the ...

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

Chapter
Section

### Mathematical Applications for the ...

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

# Retirement benefits The monthly benefit B (in thousands of dollars) from a retirement account that is invested at 9% compounded monthly is a function of the account value V (also in thousands of dollars) and the number of years t that benefits are paid, and it can be approximated by B = f ( V , t ) = 3 V 400 − 400 e − 0.0897 t (a) Find the benefit if the account value is $1,000,000 and the monthly benefits last 20 years.(b) Find and interpret ∂ B ∂ V ( 1000 , 20 ) . (b) Find and interpret ∂ B ∂ t ( 1000 , 20 ) . (a) To determine To calculate: The benefit if the account value is$1,000,000 and the monthly benefits which is compounded monthly at a rate of 9% is last for 20 years.

Explanation

Given Information:

The account value is $1,000,000 and the monthly benefits which is compounded monthly at a rate of 9% is last for 20 years. The monthly benefits B as a function of account value V is given as, B=3V400âˆ’400eâˆ’0.0897t Calculation: Consider the monthly benefits B (in thousands of dollars) as a function of account value V, B=3V400âˆ’400eâˆ’0.0897t Also, the account value is$1,000,000 and the monthly benefits last 20 years.

That is, the account value V is 1,000 thousand dollars and the number of years is 20.

Thus, the provided point is (V,t)=(1000,20).

Substitute 1000 for V and 20 for t in B=3V400âˆ’400eâˆ’0

(b)

To determine

To calculate: The value of BV(1000,20) and interpret the result if the monthly benefits B as a function of account value V is, B=3V400400e0.0897t.

(c)

To determine

To calculate: The value of Bt(1000,20) and interpret the result if the monthly benefits B as a function of account value V is, B=3V400400e0.0897t.

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