If we know the single amount (PV), the interest rate (i), and the number of periods of compounding (n), we can calculate the future value (FV) of the single amount. Calculations #1 through #5 illustrate how to determine the future value (FV) through the use of future value factors.
Calculation #1
You make a single deposit of $100 today. It will remain invested for 4 years at 8% per year compounded annually.What will be the future value of your single deposit at the end of 4 years?
The following timeline plots the variables that are known and unknown:
Calculation using an FV factor:
At the end of 4 years, you will have $136 in your account.
Calculation #2
Paul makes a single deposit today of $200. The deposit will be invested for 3 years at an interest rate of 10% per year compounded semiannually. What will be the future value of Paul's account at the end of 3 years?
The following timeline plots the variables that are known and unknown:
Because the interest is compounded semiannually, we convert 3 years to 6 semiannual periods, and the annual interest rate of 10% to the semiannual rate of 5%.
Calculation using an FV factor:
At the end of 3 years, Paul will have $268 in his account.
Calculation #3
Sheila invests a single amount of $300 today in an account that will pay her 8% per year compounded quarterly. Compute the future value of Sheila's account at the end of 2 years.
The following timeline plots the variables that are known and unknown:
Because interest is compounded quarterly, we convert 2 years to 8 quarters, and the annual rate of 8% to thequarterly rate of 2%.
Calculation using an FV factor:
At the end of 2 years, Sheila will have $351.60 in her account.
Calculation #4
You invest $400 today in an account that earns interest at a rate of 12% per year compounded monthly. What will be the future value at the end of 2 years?
The following timeline plots the variables that are known and unknown:
Because the interest is compounded monthly, we convert 2 years to 24 months, and the annual rate of 12% to the monthly rate of 1%.
Calculation using an FV factor:
At the end of 2 years, you will have $508 in your account.
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As an enthusiast with a deep understanding of financial concepts and calculations, let's delve into the specifics of the article you provided. My expertise in financial mathematics and interest compounding will be evident as we explore the intricacies of the future value calculations described in the content.
The article primarily revolves around the concept of future value (FV) and how it can be calculated based on the present value (PV), interest rate (i), and the number of compounding periods (n). The use of future value factors is highlighted, and the calculations are demonstrated through various scenarios.
Now, let's break down each calculation:
Calculation #1:
- PV: $100
- Interest rate: 8% per year
- Compounding: Annually for 4 years
- Future Value Factor used to calculate FV: Resulting in $136 at the end of 4 years.
Calculation #2:
- PV: $200
- Interest rate: 10% per year
- Compounding: Semiannually for 3 years (converted to 6 semiannual periods)
- Future Value Factor used to calculate FV: Resulting in $268 at the end of 3 years.
Calculation #3:
- PV: $300
- Interest rate: 8% per year
- Compounding: Quarterly for 2 years (converted to 8 quarters)
- Future Value Factor used to calculate FV: Resulting in $351.60 at the end of 2 years.
Calculation #4:
- PV: $400
- Interest rate: 12% per year
- Compounding: Monthly for 2 years (converted to 24 months)
- Future Value Factor used to calculate FV: Resulting in $508 at the end of 2 years.
In each case, the timeline is plotted with the known variables such as the initial deposit, interest rate, and compounding frequency. The conversion of time periods to match the compounding frequency is a crucial step, as demonstrated when converting years to semiannual periods, quarterly periods, or monthly periods.
These calculations showcase a clear understanding of the time value of money and the impact of compounding on future values. The use of Future Value factors streamlines the process, making it more accessible for financial analysis. If you have any specific questions or if there's a particular aspect you'd like to explore further, feel free to ask.
