Use the Future Value Formula to Find the Indicated Value

Oct 13, 2025 by miodeya.com 9 views

**Understanding the Future Value Formula: A Comprehensive Guide** ===========================================================

What is the Future Value Formula?

The future value formula is a mathematical concept used to calculate the future value of an investment or a series of investments. It takes into account the present value, interest rate, and time period to determine the future value of the investment. The formula is widely used in finance, economics, and other fields to make informed decisions about investments and savings.

The Future Value Formula: FV = PV x (1 + r)^n

Where:

FV = Future Value
PV = Present Value (initial investment)
r = Interest Rate (annual interest rate)
n = Number of Years

Use the Future Value Formula to Find the Indicated Value

Problem: Find the Future Value

n = 22; i = 0.03; PMT = $73; FV = ?

Solution

To find the future value, we need to rearrange the formula to solve for FV:

FV = PV x (1 + r)^n

Since we are given the interest rate (i) and the number of years (n), we can substitute these values into the formula:

FV = PV x (1 + 0.03)^22

However, we are not given the present value (PV). To find the present value, we need to use the formula:

PV = FV / (1 + r)^n

But we are trying to find the future value (FV). Let's try to find the present value first.

Find the Present Value

We are given the monthly payment (PMT) and the interest rate (i). We can use the formula for the present value of an annuity:

PV = PMT x [(1 - (1 + i)^(-n)) / i]

Substituting the given values, we get:

PV = $73 x [(1 - (1 + 0.03)^(-22)) / 0.03]

PV ≈ $1,444.19

Find the Future Value

Now that we have the present value (PV), we can substitute it into the formula:

FV = PV x (1 + r)^n

FV = $1,444.19 x (1 + 0.03)^22

FV ≈ $6,331.19

Therefore, the future value of the investment is approximately $6,331.19.

Q&A: Frequently Asked Questions

Q: What is the future value formula?

A: The future value formula is a mathematical concept used to calculate the future value of an investment or a series of investments.

Q: What are the variables in the future value formula?

A: The variables in the future value formula are:

FV = Future Value
PV = Present Value (initial investment)
r = Interest Rate (annual interest rate)
n = Number of Years

Q: How do I use the future value formula to find the future value?

A: To find the future value, you need to rearrange the formula to solve for FV. If you are given the present value (PV), you can substitute it into the formula. If you are given the monthly payment (PMT) and the interest rate (i), you can use the formula for the present value of an annuity to find the present value (PV).

Q: What is the present value of an annuity?

A: The present value of an annuity is the present value of a series of equal payments made at regular intervals.

Q: How do I calculate the present value of an annuity?

A: To calculate the present value of an annuity, you can use the formula:

PV = PMT x [(1 - (1 + i)^(-n)) / i]

Q: What is the future value of an annuity?

A: The future value of an annuity is the future value of a series of equal payments made at regular intervals.

Q: How do I calculate the future value of an annuity?

A: To calculate the future value of an annuity, you can use the formula:

FV = PV x (1 + r)^n

Q: What is the interest rate (r)?

A: The interest rate (r) is the annual interest rate.

Q: What is the number of years (n)?

A: The number of years (n) is the time period over which the investment is made.

Q: What is the monthly payment (PMT)?

A: The monthly payment (PMT) is the amount paid each month.

Q: What is the present value (PV)?

A: The present value (PV) is the initial investment.

Q: What is the future value (FV)?

A: The future value (FV) is the future value of the investment.

Conclusion

The future value formula is a powerful tool used to calculate the future value of an investment or a series of investments. By understanding the variables and how to use the formula, you can make informed decisions about investments and savings. Remember to always use the correct formula and variables to ensure accurate results.

References

[1] Investopedia. (2022). Future Value Formula.
[2] Wikipedia. (2022). Future Value.
[3] Khan Academy. (2022). Future Value and Present Value.

Additional Resources

[1] Future Value Calculator. (2022). Investopedia.
[2] Present Value Calculator. (2022). Investopedia.
[3] Future Value Formula. (2022). Wikipedia.