Chapter 3 Time Value of Money

Simple Interest Formula

• Formula SI = P0(i)(n)
• SI: Simple Interest
• P0: Deposit today (t=0)
• i: Interest Rate per Period
• n: Number of Time Periods

Simple Interest Example

• SI = P0(i)(n) = $1,000(0.07)(2) = $140

• Assume that you deposit $1,000 in an account earning 7% simple interest for 2 years. What is the accumulated interest at the end of the 2nd year?

Simple Interest (FV)

• FV = P0 + SI = $1,000 + $140 = $1,140
• Future Value is the value at some future time of a present amount of money, or a series of payments, evaluated at a given interest rate.

• What is the Future Value (FV) of the deposit?

Simple Interest (PV)

• The Present Value is simply the $1,000 you originally deposited. That is the value today!
• Present Value is the current value of a future amount of money, or a series of payments, evaluated at a given interest rate.

• What is the Present Value (PV) of the previous problem?

Why Compound Interest?

• Future Value (U.S. Dollars)

Future Value Single Deposit (Graphic)

• Assume that you deposit $1,000 at a compound interest rate of 7% for 2 years.

• 0 1 2

• $1,000

• FV2

• 7%

Future Value Single Deposit (Formula)

• FV1 = P0 (1 + i)1 = $1,000 (1.07) = $1,070
• Compound Interest
• You earned $70 interest on your $1,000 deposit over the first year.
• This is the same amount of interest you would earn under simple interest.