How to Find Interest Rate Given PV and FV
In financial calculations, determining the interest rate is a crucial step when dealing with present value (PV) and future value (FV). The interest rate represents the cost of borrowing or the return on investment over a specific period. This article will guide you through the process of finding the interest rate given the present value and future value of an investment.
The formula to calculate the interest rate is derived from the compound interest formula:
\[ FV = PV \times (1 + r)^n \]
where:
– \( FV \) is the future value
– \( PV \) is the present value
– \( r \) is the interest rate
– \( n \) is the number of periods
To find the interest rate, you can rearrange the formula as follows:
\[ r = \left( \frac{FV}{PV} \right)^{\frac{1}{n}} – 1 \]
Now, let’s explore the steps to calculate the interest rate using this formula:
1. Identify the values: First, you need to identify the present value (PV) and future value (FV) of the investment, as well as the number of periods (n).
2. Calculate the ratio: Divide the future value (FV) by the present value (PV) to get the ratio.
3. Find the nth root: Calculate the nth root of the ratio, where n is the number of periods.
4. Subtract 1: Subtract 1 from the result obtained in step 3.
5. Convert to percentage: Multiply the result by 100 to express the interest rate as a percentage.
Let’s illustrate this with an example:
Suppose you have an investment with a present value (PV) of $10,000 and a future value (FV) of $15,000 after 5 years. To find the interest rate, follow these steps:
1. Identify the values: PV = $10,000, FV = $15,000, and n = 5.
2. Calculate the ratio: \( \frac{FV}{PV} = \frac{15,000}{10,000} = 1.5 \).
3. Find the nth root: \( (1.5)^{\frac{1}{5}} \approx 1.0723 \).
4. Subtract 1: \( 1.0723 – 1 = 0.0723 \).
5. Convert to percentage: \( 0.0723 \times 100 = 7.23\% \).
Therefore, the interest rate for this investment is approximately 7.23%.
In conclusion, finding the interest rate given the present value and future value of an investment is a straightforward process. By following the steps outlined in this article, you can calculate the interest rate and gain valuable insights into the investment’s performance.
