   Chapter 14, Problem 24RE 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

Savings plans The accumulated value A of a month savings plan over a 20-year period is a function of the monthly contribution R and the interest rate r% compounded monthly, according to A = f ( R , r ) = 1200 R [ ( 1 + r 1200 ) 240 − 1 ] r (a) Find the accumulated value of a plan that contributes $100 per month with interest rate 6%.(b) Interpret f ( 250 , 7.8 ) ≈ 143 , 648 .(c) Interpret ∂ A ∂ r ( 250 , 7.8 ) ≈ 17 , 770 .(d) Find ∂ A ∂ R ( 250 , 7.8 ) and interpret the result. (a) To determine To calculate: The accumulated value of a plan that contributes$100 per month with interest rate 6%. The accumulated value A of a monthly savings plan over a 20-year period is a function of the monthly contribution R and the interest rate r% compounded monthly, according to, A=f(R,r)=1200R[(1+r1200)2401]r.

Explanation

Given Information:

The accumulated value A of a monthly savings plan over a 20-year period is a function of the monthly contribution R and the interest rate r% compounded monthly, according to,

A=f(R,r)=1200R[(1+r1200)2401]r.

Also, the plan contributes $100 per month with interest rate 6%. Formula used: The value of a function of two variables f(x,y) at the point (x,y)=(a,b) is f(a,b). Calculation: Consider the problem, the accumulated value A of a monthly savings plan over a 20-year period is a function of the monthly contribution R and the interest rate r% compounded monthly, according to; A=f(R,r)=1200R[(1+r1200)2401]r. Also, the plan contributes$100 per month with interest rate 6%.

That is, the monthly contribution R is \$100 and the interest rate r is 6% compounded monthly.

The provided point is (R,r)=(100,6).

Recall that, the value of a function of two variables f(x,y) at the point (x,y)=(a,b) is f(a,b)

(b)

To determine

The interpretation of f(250,7.8)143,648. The accumulated value A of a monthly savings plan over a 20-year period is a function of the monthly contribution R and the interest rate r% compounded monthly, according to;

A=f(R,r)=1200R[(1+r1200)2401]r.

(c)

To determine

The interpretation of Ar(250,7.8)17,770. The accumulated value A of a monthly savings plan over a 20-year period is a function of the monthly contribution R and the interest rate r% compounded monthly, according to;

A=f(R,r)=1200R[(1+r1200)2401]r.

(d)

To determine

To calculate: The value of AR(250,7.8). The accumulated value A of a monthly savings plan over a 20-year period is a function of the monthly contribution R and the interest rate r% compounded monthly, according to;

A=f(R,r)=1200R[(1+r1200)2401]r.

Interpret the result.

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