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Park 2

Time Value of Money (Sections 2.1-2.3). Park 2. Interest: The Cost of Money. Money is a commodity, and like other goods that are bought and sold, money costs money.

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Park 2

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  1. Time Value of Money (Sections 2.1-2.3) Park 2

  2. Interest: The Cost of Money • Money is a commodity, and like other goods that are bought and sold, money costs money. • Cost of money is established and measured by an interest rate, a percentage that is periodically applied and added to an amount of money over a specified length of time. • Interest is the cost of having money available for use.

  3. The Time Value of Money • Money has both earning power (earning more money for its owner) and purchasing power (it can be put to work). • Since money has both of these, a dollar today has a higher value than a dollar received at some future time. • Interest versus inflation

  4. Elements of Transactions Involving Interest • Principal (P): initial amount of money invested or borrowed in a transaction. • Interest rate (i): measures the cost or price of money and is expressed as a percentage per period of time. • Interest period (n): determines how frequently interest is calculated.

  5. Elements of Transactions Involving Interest • Number of interest periods (N): a specified length of time that marks the duration of the transaction. • Plan for receipts or disbursements (An): yields a particular cash flow pattern over a specified length of time. • Future amount of money (F): results from the cumulative effects of the interest rate over a number of interest periods.

  6. Methods of Calculating Interest • Simple Interest: interest earned on only the principal amount during each interest period. • I = (i*P) * N (interest earned) • F = P (1 + i * N) (future amount of money) • Compound Interest: interest earned in each period is calculated based on the total amount at the end of the previous period (includes original principle plus accumulated interest). • F = P ( 1 + i) ^ N

  7. Economic Equivalence • Economic equivalence refers to the fact that any cash flow can be converted to an equivalent cash flow at any point in time. • The present sum is equivalent in value to future cash flows because the present sum could be invested with interest and transformed into future cash flows. • F = P ( 1 + i ) ^ N • P = F ( 1 + i ) ^ -N

  8. Interest Formulas for Single Cash Flows • Compound-Amount Factor • Given a present sum P invested for N interest periods at interest rate i, the future sum F will be the amount accumulated at the end of N periods: • Equation: F = P ( 1 + i ) ^ N • Factor Notation: P ( F/P , i , N) • Excel: = FV (i, N, 0, P)

  9. Interest Formulas for Single Cash Flows • Present-Worth Factor • Finding the present worth of a future sum through the reverse of compounding (known as discounting process). • Equation: P = F ( 1 + i ) ^ -N • Factor Notation: F ( P/F, i, N) • Excel: = PV( i, N, 0, F)

  10. Interest Formulas for Single Cash Flows • Solving for Time and Interest Rates • Solving for Interest • Trial and error • Excel: = RATE(N, 0, P, F) • Solving for Time • Excel: = NPER( i, 0, P, F)

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