JENNIFER: Again, correct! But now, I want you to prove it. So lets assume that you invest $2,000 into two different accounts, both of which earn 7% per year, and the money is invested for three years. Account A earns simple interest, while account X earns compound interest. By how much will the future value of account X exceed the future value of account A?

Here is a sheet of paper, show me how to calculate the future values of the two accounts.

DAVID: OK, let me see what I can do . . .

Future Value of Account A

Note: Account A pays simple interest.

Future ValueAA = Principal + Interest

= Principal + [(Principal x Interest Rate) x Investment Period]

= $2,000 + [($2,000 x 7%) x 3 years]

= $__________

Future Value of Account X

Note: Account X pays compound interest.

Future ValueXX = Present Value x Interest Rate Factor

= Present Value (1 + Interest Rate)NN

= $2,000 x (1 + 0.07)

= $ ________

To find the interest rate factor, you can use four different ways, including multiplying it out:

Interest Factor (1 + 0.07) x (1 + 0.07) x (1 + 0.07) = 1.2250

Or you can use exponents, and calculate it directly:

Interest Factor = (1 + 0.07) = 1.2250

The third alternative for solving the equations is to use a spreadsheet, and the fourth is to let a financial calculator perform the calculation. This requires that you know how your calculator functions and how to enter the following variables:

Input	1	3	7	2000
Keystroke	P/Y	N	I	PV	FV
Output					Answer

P/Y indicates the number of compounding periods per year, N is the number of years, I is the interest rate, PV is present value, and FV is future value.

Difference in Future Values

Difference = FVXX FVAA

= $ __________