Question

A. Use the appropriate formula to determine the periodic depositB. How much of the financial goal comes from deposits and how much comes from interest?

Answer 1

For the given question, the formula to determine the periodic deposit will be:

$A=\frac{P((1+\frac{r}{n})^{nt^{}}-1)}{\frac{r}{n}}$

Given:

A= $1,000,000

r = 8.25% = 0.0825

Componded monthly, n = 12

time = t = 40 years

We will substitute with the given values and find the value of P

So,

$\begin{gathered} 1000000=\frac{P\cdot((1+\frac{0.0825}{12})^{12\cdot40}-1)}{\frac{0.0825}{40}} \\ 1000000=P\cdot12,513.06881 \\ \\ P=\frac{1000000}{12513.06881}=79.916 \end{gathered}$

Rounding to the nearest dollar

so, The periodic deposit = $80

Part (b): we will find the amount comes from the deposit and the amount comes from the interest

The amount of money comes from deposit = 80 * 12 * 40 = $38,400

The amount comes from the interest = 1000000 - 38400 = $961600