Question

A lottery winner invested $30,000 in an account earning 7% per year compounded continuously. If no withdrawals are made, how much was in the account at the end of five years

Answer 1

$42,572 was in the account at the end of five years

Explanation:

The amount of money, after t years, compounded continuously, is given by the following equation:

`P(t) = P(0)e^(rt)`

In which P(0) is the initial investment and r is the interest rate, as a decimal.

A lottery winner invested $30,000 in an account earning 7% per year compounded continuously.

This means that
`P(0) = 30000, r = 0.07`.

If no withdrawals are made, how much was in the account at the end of five years

This is P(5)

`P(t) = P(0)e^(rt)`

`P(5) = 30000e^(0.07*5)`

`P(5) = 42572`

$42,572 was in the account at the end of five years