Kembara’s Financial Solutions - The Effective Annual Rate is Calculated
As shown in the prior case, the annual quoted percentage on borrowing can differ significantly from the actual annual rate of borrowing. The following formula can be used to determine the effective yearly rate from the annual quoted percentage: Referring back to the loan from ABC Bank with quarterly interest payments based on a stated rate of 10% pa Step 1: Determine the interest rate that will be applied for each time period that the loan specifies. Since the loan has quarterly interest payments, the quarterly interest rate is equal to the annual rate of 10% divided by 4. (because there are four quarters in each year). Interest is levied quarterly at a rate of 10% divided by 4, or 2.5 percent. Step 2: Using the rate determined in Step 1 and assuming no interest is paid during the year, determine how much will be owing at the end of the year given a loan of £100 at the start of the year. At the start of the year, the loan's starting balance was £100. 100 multiplied by 2.5% to equal £2.50 in interest at the conclusion of the first quarter. Assuming no interest has been paid, the loan's starting balance at the beginning of the second quarter is £102.50 ($100 + £2.50). At the end of the second quarter, interest was levied at the rate of £2.56 per £102.50. (rounded to the nearest penny). Assuming no interest has been paid, the loan's starting balance at the beginning of the third quarter is £105.06, or £102.50 plus £2.56. By multiplying £105.06 by 2.5% at the conclusion of the third quarter, interest came to £2.63. (rounded to the nearest penny). Assuming no interest has been paid, the loan's starting balance at the beginning of the fourth quarter is £105.06 plus £2.63, or £107.69. By multiplying £107.69 by 2.5% at the conclusion of the fourth quarter, interest came to £2.69. (rounded to the nearest penny). If no interest has been paid, the loan balance at the end of the year will be £107.69 plus £2.69, which equals £110.38. Step 3: Determine the annual effective interest rate using the loan's final balance from Step 2's calculation. Starting balance less ending balance is £100.38 - £100.00, or the annual effective interest rate, which is $10.38. Step 4: Calculate the effective annual rate by converting the effective interest charged to a percentage of the initial sum. Effective interest is calculated as £10.38 divided by £100.00, or 0.1038. For a percentage, multiply by 100: 0.1038 x 100 = 10.38%. IMPORTANT: UK sterling (pounds or $) is divided into 100 pence, or one penny, which is denoted by the letter "p." 100 cents, also represented by the letters "c" or "," are equal to one US dollar ($). Exercise 2: Effective Annual Rate Calculation Example An alternative method for figuring up the effective yearly rate is: Step 1: Determine the interest rate that will be applied for each time period that the loan specifies. This is a quarterly charge of 10% p.a. The rate is 10/4, or 2.5%, each quarter because there are four quarters in a year. Step 2: Divide the rate from Step 1 by 100 to express it as a decimal. 2.5/100 is 0.025. Step 3: Multiply the result from Step 2 by the number of times interest will be paid over the course of the year, then add the number 1 to the result. 1 + 0.025 = 1.025. Given that interest is calculated quarterly, 1.025 multiplied by itself four times results in 1.1038. Note: Another way to write 1.025 x 1.025 x 1.025 is (1.025 'to the power of 4'). Step 4: Subtract 1 from the result of Step 3 and multiply the result by 100 to express the result as a percentage. 1.1038 – 1 = 0.1038 0.1038 x 100 = 10.38%.
0 Comments
Leave a Reply. |
AuthorAnything you need to know about finance, money and business Archives
May 2023
Categories
All
|