When analyzing a loan or investment, you may find it difficult to clearly understand the true cost of the loan or the true return on the investment. There are several terms that are used when talking about the interest rate or return, including annual percentage return, annual rate, effective, nominal, and more. Of these, the effective interest rate is probably the most useful, as it provides a relatively complete picture of the true cost of borrowing. To calculate it on a loan, you first need to understand the terms defined by the loan and perform a simple calculation.
Steps
Part 1 of 2: Getting the Information You Need
Step 1. Familiarize yourself with the concept of an effective interest rate
This term describes the entire cost of money which takes into account the effect of the compounding of interest, which instead is usually excluded from the nominal or "declared" interest rate.
- For example, a loan with 10% monthly compound interest will actually cost a lot more than this percentage, since a share of interest is compounded every month.
- The calculation of the effective interest rate does not take into account the one-off fees which constitute an initial cost of the loan. However, these expenses are included in the calculation of the overall annual rate.
Step 2. Determine the declared interest rate
This rate (also called nominal) is expressed as a percentage.
The nominal interest rate represents the "base" value from which to start calculating the true cost of money. This is the rate that is typically advertised by the finance company
Step 3. Determine the number of loan compounding periods
Usually these are monthly, quarterly, yearly or continuous and refer to how often the interest is applied.
The compounding periods are usually on a monthly scale. However, you must check the loan agreement with the company that provided it
Part 2 of 2: Calculate the Effective Interest Rate
Step 1. Learn the formula for converting nominal interest rate to effective rate
This is obtained from the simple equation: r = (1 + i / n) ^ n - 1.
In this formula, r represents the effective interest rate, i the nominal rate, and n the number of annual compounding periods
Step 2. Calculate the effective interest rate with the formula just described
For example, consider a loan with a nominal interest rate of 5% that is compounded monthly. Using the equation you get: r = (1 + 0, 05/12) ^ 12 - 1, i.e. r = 5, 12%. The same loan with daily compounding periods would have a yield of: r = (1 + 0, 05/365) ^ 365 - 1, i.e. r = 5.13%. You can see that the effective interest rate is always higher than the nominal one.
Step 3. Learn the formula for calculating continuous compound interest
In this case you should use the compound interest rate with another equation: r = e ^ i - 1, where r is the effective interest rate, i is the nominal one and e is a constant equal to 2,718.
Step 4. Calculate the effective interest rate in the case of continuous compound interest
For example, consider a 9% nominal rate loan that is compounded continuously. The above formula leads you to this calculation: r = 2.718 ^ 0, 09 - 1, i.e. 9.417%.
