Chapter 10.4, Problem 1E

A Retirement Account refer toExample 1

a. How fast was the amount in the account growing when it reached? $\$30,000?$

b. How much money was in the account when it was growing at twice the rate of your annual contribution?

c. How long do you have to wait for the money in the account to reach $\$40,000$?

Example 1: A Retirement Account

You invest in a retirement account that pays $6\%$ interest per year. You make an initial deposit of $\$1000$ and plan on making future deposits at the rate of $\$2400$ per year. Assume that the deposits are made continuously and that interest is compounded continuously. Let $P\left(t\right)$ denote the amount of money in the account $t$ years after the initial deposit.

a. Set up an initial-value problem that is satisfied by $P\left(t\right)$.

b. Find $P\left(t\right)$.