Question

Suppose you want to have $400,000 for retirement in 35years. Your account earns 4% interest.

Answer 1

$\begin{equation*} \ 437.76 \end{equation*}$

1) This is a question for Annuity usage. Note that we'll need the following formula below:

$\begin{gathered} P=\frac{A(\frac{r}{n})}{\lbrack(1+\frac{r}{n})^{nt}-1\rbrack} \\ P=\frac{400000(\frac{0.04}{12})}{\lbrack(1+\frac{0.04}{12})^{12\cdot35}-1\rbrack} \\ P=\frac{400000\cdot\frac{0.04}{12}}{\left(1+\frac{0.04}{12}\right)^{35\cdot\:12}-1} \\ P=\frac{400000\cdot\frac{0.04}{12}}{1.0033^{420}-1} \\ P=437.76563...\approx\ 437.76 \end{gathered}$

Note that P is the value you'll need to deposit each month so that in 35 years you'll have $400,000 for your retirement.