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Future Value (FV)
The value an amount of money invested today will grow to at a future date.
Present Value (PV)
The current value today of an amount of money to be received in the future.
Period Interest Rate (r)
The interest rate earned or charged during each period.
Number of Periods (t)
The amount of time over which money earns interest or is discounted.
Compounding
Earning interest on previously earned interest.
Effect of Compounding
Compounding has a greater effect as the number of periods increases.
Discounting
Finding the present value of a future amount of money.
Discount Rate
The interest rate used to determine the value of money across time.
Implied Interest Rate
The rate of return that connects a present amount to a future amount over a given period.
Rule of 72
A quick method for estimating how long it will take an investment to double.
Natural Logarithm (ln)
A mathematical function used when solving for the number of periods.
Time Value of Money
The principle underlying PV and FV: money changes in value across time because it can earn interest.
Uneven Cash Flows
A stream of payments in which the amount varies from one period to the next.
Cash Flow
An amount of money received or paid at a particular point in time.
Cash-Flow Timeline
A visual representation showing when individual cash flows occur.
Year 0
The present point in time—today.
Present Value of Uneven Cash Flows
The value today of multiple unequal cash flows occurring at different times.
Future Value of Uneven Cash Flows
The value at a future date of multiple unequal cash flows occurring at different times.
Discounting Uneven Cash Flows
Moving each future cash flow backward to the present.
Compounding Uneven Cash Flows
Moving each cash flow forward to a specified future date.
Target Date
The point in time to which cash flows are being moved for valuation.
Earlier Cash Flow
A cash flow that has more time to compound when calculating a future value.
Later Cash Flow
A cash flow that undergoes less compounding when moved to the same future date.
Interest Rate ↑ → Future Value
Future value increases.
Time ↑ → Future Value
Future value increases when the interest rate is positive.
Discount Rate ↑ → Present Value
Present value decreases.
Time Until Payment ↑ → Present Value
Present value decreases when the discount rate is positive.
Interest Rate ↑ → Doubling Time
The amount of time needed to double your money decreases.
More Time to Reach Same FV → Required Rate
The required interest rate decreases.
Less Time to Reach Same FV → Required Rate
The required interest rate increases.