Intro to time value of money; future value
Introduction to Time Value of Money
Overview of Interest Rates
- The video begins with a recap of the previous discussion on interest rates, emphasizing their role as the price of money and differentiating between simple and compound interest.
- Introduction of a new concept: the time value of money, which relates to how interest rates interact with time.
Financial Calculators
- Recommendations for financial calculators such as Calculator.net and FNCalc.com are provided, highlighting their usefulness in understanding financial concepts.
- The speaker prepares to take notes while switching between the calculators for practical demonstrations.
Understanding Time Value of Money
Key Concepts
- A dollar today is worth more than a dollar in the future due to its potential growth through investment. This principle underpins the time value of money.
- An example illustrates that receiving $100 today is preferable over receiving it next year because it can be invested or saved.
Important Terms
- Future Value (FV):
- Defined as how much an amount will grow over time at a certain interest rate. It can also refer to what you expect to receive in the future.
- Present Value (PV):
- Represents what you have now or how much future money is worth today. It helps understand how much needs to be invested now to achieve a desired future sum.
Compounding and Discounting
Movement Through Time
- Compounding refers to growing present value into future value, while discounting pulls future value back into present terms.
Additional Components
- Interest Rate (I):
- Denoted as I or IY (interest per year), crucial for calculating both FV and PV.
- Number of Periods (N):
- Refers to how long the investment will grow or be discounted.
Payments and Annuities
Understanding Payments
- Payment (PMT):
- In finance, PMT refers specifically to equal cash flows either coming in or going out rather than just any payment made.
Concept of Annuity
- Annuity:
- Defined as a series of payments made at regular intervals; essential when discussing investments like retirement accounts.
Calculating Future Value
Example Calculation
- A scenario where $5,000 is invested at 5% for 40 years demonstrates how compounding works using formulas or calculators.
- The formula used is FV = PV * (1 + r)^n where r is the interest rate and n is number of periods.
- Using a financial calculator simplifies this process by allowing users to input known variables directly without complex calculations.
Doubling Your Investment
New Scenario Analysis
- A new problem involves determining how long it takes $10,000 at 7% interest to double.
- The approach remains consistent: identify known variables and solve for N using financial calculators.
Future Value with Annuities
Roth IRA Example
- Starting contributions into a Roth IRA at age 22 with annual deposits shows long-term benefits from consistent investing over time.
- Contributions are set at $6,000 annually with an expected return rate leading up to retirement after 45 years.
Monthly Contributions Adjustment
Transition from Annual to Monthly Contributions
- Adjustments must be made when changing contribution frequency from yearly ($6,000 once per year) to monthly ($500 per month).
- This requires recalculating N by multiplying by months per year and adjusting I accordingly for monthly compounding effects.
Conclusion on Time Value Calculations
Summary Insights
- Emphasizes that even small changes in contribution frequency can significantly impact total returns due to compounding effects over time.
- Different calculators may yield slightly different results based on rounding but provide valuable tools for understanding these concepts effectively.