Question

Asked Jul 10, 2019

Assume a person invests $12000 at the end of each year for 30 years at an annual interest rate of r. The amount of money after 30 years is (see figure)

Assume a person wants $1000000 in the account after 30 years.

a. Shwo the minimum value of r required to meet the person's investment needs satisfieds the following equation

1,000,000r - 12,000(1+r)^30 + 12,000 = 0

b. Apply Newton's method to solve the equation in part (a) to find the interest rate required to meet the person's investment goal.

Step 1

Part (a)

The future value amount should be equal to A = $ 1,000,000.

Please see the white board.

The minimum value of r required to meet the person's investment needs should satisfy the equation on the white board and hence it must be a solution of this equation.

Step 2

Part (b)

Before we get into solving the equation by Newton's method, let's understand the method a little bit better.

If x_{n} is an approximate solution of F(x) and F’(x_{n}) ≠ 0 then the next approximate solution x_{n+1} is given by the expression on the White Board.

Step 3

Let's select F(x) to be: F(x) = 1,000,000x – 12,000(1+x)30 + 12,000

Please note that it'sthe same function as derived in part (a). We have simply replaced "r" by "x".

Hence, F’(x) = 1,000,000 –...

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