Question

Samuel invested $28,000 in an account paying an interest rate of 5% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 5 years?

Answer 1

$35,953 would be in the account after 5 years.

Explanation:

The amount of money earned in interest which is compound continuosly after t years is given by the following equation:

`A(t) = Pe^(rt)`

In which A(t) is the amount of money after t years, P is the principal(initial deposit) and r is the interest rate, as a decimal.

Samuel invested $28,000 in an account paying an interest rate of 5% compounded continuously.

This means that
`P = 28000, r = 0.05`

So

`A(t) = Pe^(rt)`

`A(t) = 28000e^(0.05t)`

How much money, to the nearest dollar, would be in the account after 5 years?

This is A(5)

`A(t) = 28000e^(0.05t)`

`A(5) = 28000e^(0.05*5) = 35952.7`

Rounding up to the nearest dollar

$35,953 would be in the account after 5 years.