Future Value and Compound Interest

This module is focused on understanding the future value of a lump sum for a single period.
The content covers concepts related to financial assessments, specifically for a single cash flow.

Future Value (FV): The future value represents the worth of a certain amount of money at a future date after taking into account the interest earned over a specified period.
- Example: If you have $100 today, you might want to know how much it will be worth one year from now considering interest accumulation.
The future value is calculated to determine how much an asset today will grow to considering the interest applied over time.

Compound Interest: This is a method of calculating interest where interest is added to the principal amount, allowing subsequent interest calculations to be based on the new total.
- It includes both the initial principal and the interest that has been added.
The concept of compound interest is crucial for evaluating the attractiveness of an investment and allows for comparison between different investment options.
It also helps to understand the impact of inflation on future costs of many assets, such as real estate or vehicles.

Future value calculations are important for projecting how much investments will grow over time under various interest scenarios.
It can also illustrate the effects of inflation, as in determining how much a house might be worth in 10 years under a certain inflation rate.

The basic formula to calculate future value is: $FV = PV imes (1 + r)$ where:
- FV is the future value.
- PV is the present value (value today).
- r is the interest rate (expressed as a decimal).

Initial Deposit (Present Value):
- Jan deposits $200 today.
Interest Rate:
- The account pays an interest rate of 6% per year.
Compounding Frequency:
- The cash flows are analyzed at the end of the year.

To find out how much Jan will have at the end of one year, we apply the formula and also show the calculation step-by-step:

Determine the Interest Earned:
- Interest earned in one year:
  $200 imes 0.06 = 12$
Future Value Calculation:
- Applying the formula:
  $FV = 200 imes (1 + 0.06)^1$
- Performing the calculation:
  $FV = 200 imes 1.06 = 212$

This example demonstrates the straightforward nature of future value calculations for a single cash flow over one compounding period.
Understanding future value helps in making informed decisions regarding savings and investments, particularly with respect to expected rates of return.