Chapter 14, Problem 24RE

(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, $\begin{array}{c}A=f\left(R,r\right)\\ =\frac{1200R\left[{\left(1+\frac{r}{1200}\right)}^{240}-1\right]}{r}\end{array}$.

(b)

To determine

The interpretation of $f\left(250,7.8\right)\approx 143,648$. 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;

$\begin{array}{c}A=f\left(R,r\right)\\ =\frac{1200R\left[{\left(1+\frac{r}{1200}\right)}^{240}-1\right]}{r}\end{array}$.

(c)

To determine

The interpretation of $\frac{\partial A}{\partial r}\left(250,7.8\right)\approx 17,770$. 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;

$\begin{array}{c}A=f\left(R,r\right)\\ =\frac{1200R\left[{\left(1+\frac{r}{1200}\right)}^{240}-1\right]}{r}\end{array}$.

(d)

To determine

To calculate: The value of $\frac{\partial A}{\partial R}\left(250,7.8\right)$. 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;

$\begin{array}{c}A=f\left(R,r\right)\\ =\frac{1200R\left[{\left(1+\frac{r}{1200}\right)}^{240}-1\right]}{r}\end{array}$.

Interpret the result.