In analyzing a loan or investment, a clear picture of the original cost of the loan or the real return on investment is quite difficult to obtain. There are several different terms used to describe the interest rate or yield on a loan, including annual yield percentage, annual interest rate, effective interest rate, nominal interest rate, and so on. Of all these terms, the effective interest rate is probably the most useful because it can provide a relatively complete picture of the true cost of borrowing. To calculate the effective interest rate on a loan, you need to understand the terms stated in the loan agreement and perform simple calculations.
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Part 1 of 2: Gathering the Necessary Information
Step 1. Understand the concept of the effective interest rate
The effective interest rate attempts to explain the full cost of the loan. This interest rate takes into account the effect of compound interest, which is ignored in nominal or “written” interest rates.
- For example, a loan with an interest rate of 10% compounded monthly actually has an interest rate greater than 10% because the interest earned is accumulated each month.
- The calculation of the effective interest rate does not take into account single-load costs, such as the initial cost of a loan. However, these costs are taken into account in calculating the annual percentage.
Step 2. Determine the nominal interest rate
The written interest rate (nominal) is presented as a percentage.
Written interest rates are usually the “headline” of interest rates. This figure is usually advertised by lenders as the interest rate
Step 3. Determine the number of loan compounding periods
The compounding period is usually monthly, quarterly, yearly, or continuous. This refers to how often interest is applied.
Usually, compounding is done monthly. However, you should check with creditors to be sure
Part 2 of 2: Calculating the Effective Interest Rate
Step 1. Understand the formula for converting written interest rates to effective interest rates
The effective interest rate is calculated using a simple formula: r = (1 + i/n)^n - 1.
In this formula, r represents the effective interest rate, i represents the nominal interest rate, and n represents the number of compounding periods per year
Step 2. Calculate the effective interest rate using the formula above
For example, let's say a loan with a nominal interest rate of 5% is compounded monthly. Using the formula, we get: r = (1 + 0, 05/12)^12 - 1, or r = 5, 12%. A loan equal to daily compounding would yield: r = (1 + 0.05/365)^365 - 1, or r = 5, 13%. It should be noted that the effective interest rate will always be greater than the nominal interest rate.
Step 3. Understand the formula for continuous compound interest
If interest is compounded continuously, we recommend that you calculate the effective interest rate using a different formula: r = e^i - 1. Using this formula, r is the effective interest rate, i is the nominal interest rate, and e is a constant of 2.718.
Step 4. Calculate the effective interest rate for continuously compounded interest
For example, let's say a loan with a nominal interest rate of 9% is compounded continuously. The formula above returns: r = 2.718^0, 09 - 1, or 9.417%.
Step 5. Simplify the calculations after reading and understanding the theory
- Once you understand the theory, do the calculations in another way.
- Find the number of intervals in a year, 2 for bianual, 4 for quarter, 12 for monthly, and 365 for daily.
- The number of intervals each year x 100 plus the interest rate. If the interest rate is 5%, that means 205 for biennial compounding, 405 for quarterly, 1205 for monthly, 36505 for daily.
- Effective interest is a value that exceeds 100 if the principal is equal to 100.
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Do the calculation as follows:
- ((205÷200)^2)×100 = 105, 0625
- ((405÷400)^4)×100 = 105, 095
- ((1, 205÷1, 200)^12)×100=105, 116
- ((36, 505÷36, 500)^365)×100 = 105, 127
- A value exceeding 100 in example (a) is the effective interest rate if compounding is done manually. Thus, 5.063 is the effective interest rate for manual compounding, 5.094 for quarter, 5, 116 for monthly, and 5, 127 for daily.
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Just remember it in theoretical form.
(Number of intervals x 100 plus interest) divided by (sum of intervals x 100) to the power of the number of intervals, multiply the result by 100. A value exceeding 100 is the amount of effective interest
