menu
Hit Return to see all results
Chapter 14, Problem 24RE
BuyFindarrow_forward

### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section
BuyFindarrow_forward

### 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.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

## Additional Math Solutions

#### Find more solutions based on key concepts

Show solutions add

#### In Exercises 107-120, factor each expression completely. 112. x2 2x 15

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Given that the points P(2,3) lies on the line 2x+ky+10=0, find k.

Finite Mathematics for the Managerial, Life, and Social Sciences

#### True or false:

Study Guide for Stewart's Multivariable Calculus, 8th

#### Sometimes, Always, or Never: If c is a critical number, then f′(c) = 0.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th