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**Concept of Time Value of Money (TVM):**

**Definition:**The principle that money available today is more valuable than the same amount in the future due to its potential earning capacity.**Reason:**Money can earn interest or be invested to generate returns, so receiving money now is worth more than receiving it later.

**Formulas:**

**Present Value (PV):****Formula:****Where:****FV:**Future Value (amount of money in the future)**r:**Interest Rate (annual)**n:**Number of Periods (years)

**Purpose:**To determine the current value of a future sum of money based on a specified rate of return.**Example Calculation:**If you expect to receive $10,000 in 5 years and the annual interest rate is 6%, the present value is calculated as:

**Future Value (FV):****Formula:****Where:****PV:**Present Value (initial amount of money)**r:**Interest Rate (annual)**n:**Number of Periods (years)

**Purpose:**To calculate the amount of money that an investment will grow to over time.**Example Calculation:**If you invest $5,000 today at an annual interest rate of 4% for 3 years, the future value is calculated as:

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**Annuities:****Definition:**A series of equal payments made at regular intervals.**Formulas:****Where:****PMT:**Payment amount**r:**Interest Rate (per period)**n:**Number of Periods (payments)

**Example Calculation:****PVA:**If you receive $1,000 annually for 4 years at an interest rate of 5%, the present value of the annuity is:**FVA:**If you deposit $500 annually for five years at an interest rate of 6%, the future value of the annuity is:

**Practical Applications in Investment and Financing:**

**Investment Decisions:**Use PV and FV calculations to determine the attractiveness of investment opportunities.**Loan Repayments:**Calculate loan payments and total interest paid over the life of the loan using annuity formulas.

**Interactive Calculator: Time Value of Money Calculator:**

**Objective:**Practice calculating PV, FV, and annuities using various scenarios.**Scenario:**- You plan to invest $15,000 today in a savings account that earns 3% annual interest for 10 years. Use the FV calculator to determine the amount you will have at the end of the period.
**Calculation:****Scenario:**You want to save $200 monthly for 8 years in an account that offers 5% annual interest. Use the FVA calculator to determine the future value of your savings.**Calculation:**

- You plan to invest $15,000 today in a savings account that earns 3% annual interest for 10 years. Use the FV calculator to determine the amount you will have at the end of the period.

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