(a)

Principal Amount .

Rate of interest  .

If a principal is invested at an annual interest rate  compounded continuously, then the balance in the account after years is .

Substitute and in .

.

Balance of savings account at time years compounded continuously is .

If a principal is invested at an annual interest rate  compounded times a year, then the balance in the account after years is .

The bank will match of the initial investment, the bank add to the initial amount .

Since amount is compounded annually .

Substitute , and  in .

Balance of savings account at time years annually compounded is .

(b)

Find the time at which continuously compounded is equal to the balance of savings account annually compounded.

Equate the balance of savings account annually compounded and continuously compounded.

Apply logarithm on each side.

Apply product

property of logarithm : .

Apply power property of logarithm : .

The property of logarithm is : .

.

It takes years for the continuously compounded account to catch up with the annually compounded savings account.

(c)

Find balance of savings account compounded continuously after years.

Substitute in .

 Balance of savings account at time years compounded continuously is .

Find balance of savings account annually compounded after years.

Substitute in .

Balance of savings account at time years annually compounded is . 

Balance of savings in compounded continuously account is less than annually compounded.

 Brandy choose to leave compounded continuously account.

(a)

Balance of savings account at time t years compounded continuously is .

Balance of savings account at time t years annually compounded is .

(b)

It take years for the continuously compounded account to catch up with the annually compounded savings account.

(c)

 Brandy choose to leave compounded continuously account.