4.6 Compounding techniques – Compound interest, Future value (FV) of a single cash flow and series of cash flows; Compounding of annuity cash flows

Compounding techniques are used to calculate the future value of cash flows by incorporating the concept of compound interest. Compound interest refers to the process of earning interest on both the initial principal amount and any accumulated interest from previous periods. Here are the compounding techniques commonly used:

1. Future Value (FV) of a Single Cash Flow: This technique calculates the future value of a single cash flow, assuming a certain interest rate and a specified time period. The formula for calculating the future value is:FV = PV * (1 + r)^nWhere: FV = Future value PV = Present value or initial cash flow r = Interest rate per compounding period n = Number of compounding periods

   This formula accounts for the compounding effect, allowing you to determine the value of a cash flow at a future date.

2. Future Value (FV) of a Series of Cash Flows: When there are multiple cash flows occurring over a period of time, you can calculate the future value of the entire series. Each cash flow is compounded individually to its respective future date, and then the future values are summed to determine the total future value. The formula for calculating the future value of a series of cash flows is:FV = CF₁ * (1 + r)^n₁ + CF₂ * (1 + r)^n₂ + … + CFₙ * (1 + r)^nₙWhere: FV = Future value of the series of cash flows CF₁, CF₂, …, CFₙ = Individual cash flows n₁, n₂, …, nₙ = Number of compounding periods for each cash flow r = Interest rate per compounding period

   This technique considers the compounding of each cash flow to its respective future date, reflecting the time value of money.

3. Compounding of Annuity Cash Flows: An annuity represents a series of equal cash flows occurring at regular intervals. The future value of an annuity can be calculated using the formula for the future value of a series of cash flows. However, in the case of an annuity, there is a simplified formula that accounts for the regularity of the cash flows. The formula for calculating the future value of an annuity is:FV = Pmt * [(1 + r)^n – 1] / rWhere: FV = Future value of the annuity Pmt = Payment amount (equal cash flow) r = Interest rate per compounding period n = Number of compounding periods

   This formula takes into account the compounding of the equal cash flows over time, considering the regularity of the annuity.

These compounding techniques help in evaluating the future value of cash flows, including single cash flows, series of cash flows, and annuity cash flows. By accounting for compound interest, they provide insights into the growth and accumulation of wealth over time, allowing for better financial planning and decision-making.

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