Refer to Example 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.

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(t) denote the amount of money in the account t years after the initial deposit.