Question

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

a) How much would you need to deposit in the account each month?

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=(A((r)/(n)))/(\lbrack(1+(r)/(n))^(nt)-1\rbrack) \\ P=(400000((0.04)/(12)))/(\lbrack(1+(0.04)/(12))^(12\cdot35)-1\rbrack) \\ P=(400000\cdot(0.04)/(12))/(\left(1+(0.04)/(12)\right)^(35\cdot\:12)-1) \\ P=(400000\cdot(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.