You are given three options. You may have the balance in an account that has been collecting 5 percent interest for 20 years, the balance in an account that has been collecting 10 percent interest for 10 years, or the balance in an account that has been collecting 20 percent interest for five years. Each account had the same original balance. Which account now has the lowest balance

Third account has the lowest balance that is 2.49P.

Explanation:

First option,  

Given interest rate = 5%

Time period = 20 years

Let the initial amount ( present value ) = P

First Account,  

Given interest rate (n )= 5%

Time period (n ) = 20 years

Let the initial amount ( present value ) = P

Now find the Future value = PV(1+ r)^n

= P ( 1 + 5%)^20  

= 2.65P

Second account:

Given interest rate (n ) = 10%

Time period (n ) = 100 years

Let the initial amount ( present value ) = P

Now find the Future value = PV(1+ r)^n

= P ( 1 + 10%)^10  

= 2.59P

Thirs account:

Given interest rate (n ) = 20%

Time period (n ) = 5 years

Let the initial amount ( present value ) = P

Now find the Future value = PV(1+ r)^n

= P ( 1 + 20%)^5  

= 2.49P