Select The Correct Answer.You Want To Deposit $\$ 15,000$ In A Bank At An Interest Rate Of 7 Percent Per Year. What Is The Future Value Of This Money After Three Years?Future Value $=$ P \times (1+i)^t$A. \$\$
Understanding the Concept of Future Value
In finance, the future value of an investment or deposit is the amount of money it will grow to over time, assuming a fixed interest rate. The formula for calculating future value is given by:
FV = P × (1 + i)^t
Where:
- FV is the future value of the investment
- P is the principal amount (initial deposit)
- i is the annual interest rate (in decimal form)
- t is the number of years the money is invested for
Calculating the Future Value of a Deposit
In this example, we want to deposit $15,000 in a bank at an interest rate of 7 percent per year. We need to calculate the future value of this money after three years.
Step 1: Convert the Interest Rate to Decimal Form
The interest rate is given as 7 percent per year. To convert this to decimal form, we divide by 100:
i = 7/100 = 0.07
Step 2: Plug in the Values into the Formula
Now that we have the interest rate in decimal form, we can plug in the values into the formula:
FV = P × (1 + i)^t FV = 15000 × (1 + 0.07)^3
Step 3: Calculate the Future Value
To calculate the future value, we need to evaluate the expression (1 + 0.07)^3:
(1 + 0.07)^3 = 1.07^3 = 1.221025
Now, we multiply this value by the principal amount:
FV = 15000 × 1.221025 FV = 18315.375
Rounding the Future Value
Since we are dealing with money, we typically round the future value to two decimal places:
FV ≈ $18,315.38
Conclusion
In this example, we calculated the future value of a deposit of $15,000 at an interest rate of 7 percent per year after three years. The future value of this money is approximately $18,315.38.
Common Mistakes to Avoid
When calculating future value, it's essential to avoid common mistakes such as:
- Forgetting to convert the interest rate to decimal form
- Plugging in the wrong values into the formula
- Not rounding the future value to the correct number of decimal places
Real-World Applications
Calculating future value has numerous real-world applications, such as:
- Determining the future value of investments
- Calculating the future value of retirement savings
- Evaluating the future value of business loans
Additional Resources
For more information on calculating future value, you can consult the following resources:
- Online calculators and spreadsheets
- Financial textbooks and online courses
- Professional financial advisors and consultants
Final Thoughts
Frequently Asked Questions
In this article, we'll answer some of the most common questions related to calculating future value.
Q: What is the formula for calculating future value?
A: The formula for calculating future value is given by:
FV = P × (1 + i)^t
Where:
- FV is the future value of the investment
- P is the principal amount (initial deposit)
- i is the annual interest rate (in decimal form)
- t is the number of years the money is invested for
Q: How do I convert the interest rate to decimal form?
A: To convert the interest rate to decimal form, simply divide by 100. For example, if the interest rate is 7 percent per year, you would divide by 100 to get:
i = 7/100 = 0.07
Q: What is the difference between simple interest and compound interest?
A: Simple interest is calculated as a percentage of the principal amount, while compound interest is calculated as a percentage of the principal amount plus any accrued interest. In other words, compound interest is calculated on the current balance, not just the principal amount.
Q: How do I calculate the future value of a deposit with compound interest?
A: To calculate the future value of a deposit with compound interest, you can use the formula:
FV = P × (1 + i)^t
Where:
- FV is the future value of the investment
- P is the principal amount (initial deposit)
- i is the annual interest rate (in decimal form)
- t is the number of years the money is invested for
Q: What is the difference between annual compounding and monthly compounding?
A: Annual compounding means that the interest is compounded once per year, while monthly compounding means that the interest is compounded once per month. Monthly compounding will result in a higher future value than annual compounding, since the interest is being compounded more frequently.
Q: How do I calculate the future value of a deposit with monthly compounding?
A: To calculate the future value of a deposit with monthly compounding, you can use the formula:
FV = P × (1 + i/m)^(m*t)
Where:
- FV is the future value of the investment
- P is the principal amount (initial deposit)
- i is the annual interest rate (in decimal form)
- m is the number of times the interest is compounded per year (12 for monthly compounding)
- t is the number of years the money is invested for
Q: What is the effect of inflation on future value?
A: Inflation can have a significant impact on future value, since it can erode the purchasing power of money over time. To account for inflation, you can use an inflation rate in the formula, or use a real interest rate that takes into account the effect of inflation.
Q: How do I calculate the future value of a deposit with inflation?
A: To calculate the future value of a deposit with inflation, you can use the formula:
FV = P × (1 + i - r)^t
Where:
- FV is the future value of the investment
- P is the principal amount (initial deposit)
- i is the nominal interest rate (in decimal form)
- r is the inflation rate (in decimal form)
- t is the number of years the money is invested for
Conclusion
Calculating future value is a crucial concept in finance that can help individuals and businesses make informed decisions about investments and savings. By understanding the formula and the different types of interest, you can calculate the future value of a deposit or investment with ease.