Park 2 Time Value Of Money Sections 21-23 Interest The Cost

Park 2time Value Of Money Sections 21 23interest The Cost Of Mone

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. 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 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. 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. Methods of Calculating Interest Simple Interest: interest earned on only the principal amount during each interest period. I = (iP) 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 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 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) 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) Interest Formulas for Single Cash Flows Solving for Time and Interest Rates Solving for Interest Trial and error, solve for i Excel: = RATE(N, 0, P, F) Solving for Time Trial and error, solve for N Excel: = NPER( i, 0, P, F)

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The concept of the time value of money (TVM) is fundamental in finance and economics, emphasizing that money available now is more valuable than the same amount in the future due to its potential earning capacity. This principle underpins many financial decisions, including investments, loans, and savings. Central to TVM are interest rates, which measure the cost of money over time, and the methods used to calculate growth or present value of cash flows.

Understanding the distinction between simple and compound interest is crucial. Simple interest is calculated solely on the initial principal, regardless of accumulated interest, whereas compound interest considers the accumulated amount at each period, leading to exponential growth over time. The formulas for future value and present value, expressed as F = P(1 + i)^N and P = F(1 + i)^-N respectively, are fundamental tools in financial analysis.

Economic equivalence plays an essential role, allowing the comparison of cash flows happening at different points in time by converting them to a common present or future value. This concept underlies the valuation of investments and projects, enabling decision-makers to determine which options yield the highest returns or are most financially viable.

Practical applications of these principles can be observed through typical problem-solving scenarios, such as calculating the present worth of a future payment, determining necessary interest rates to achieve savings goals, or comparing different investment options. For example, the present worth of a $9,450 payment due in five years at a 7% interest rate can be computed using the formula P = F(1 + i)^-N, which discounts the future sum to today's value using prevailing interest rates.

In addition, understanding how different interest rates impact the growth of investments is vital. If an individual invests $7,450 at 7% compounded annually, the amount accumulated over five years can be calculated by F = P(1 + i)^N. Conversely, to achieve a specific future goal, such as doubling current savings, knowing the required interest rate or the time period becomes critical, often solved using algebraic manipulations of the compound interest formula or financial functions available in tools like Excel.

Furthermore, selecting between investment options depends on their respective present or future values calculated via these formulas. For instance, receiving $2,000 today, or $3,500 after three years, or $4,000 after six years, can be compared by discounting future cash flows to present values using the interest rate, enabling a decision based on the highest equivalent value.

In practice, calculating the number of years needed to double an investment or the interest rate needed for a target future value are common tasks. These are approached through algebraic rearrangements of formulas or utilizing Excel functions such as RATE and NPER to solve iteratively for interest rates or time periods. This adaptability in calculations allows investors and financial managers to optimize their strategies based on specific goals and constraints.

In conclusion, mastery of the principles of the time value of money, including understanding interest calculations, economic equivalence, and the application of formulas for present and future values, is indispensable in financial decision-making. These tools enable accurate valuation, comparison, and forecasting, ensuring informed and effective financial strategies in various contexts.

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