Learning Objectives<\/p>\n\n<\/header>\n
- \n \t
- State the difference between nominal and effective interest rates<\/li>\n \t
- Determine the effective annual interest rate<\/li>\n \t
- Determine the best option when comparing nominal interest rates under different situations<\/li>\n<\/ul>\n<\/div>\n<\/div>\n
Nominal and Effective Rates of Interest<\/strong><\/h1>\nAs consumers and investors we are inundated with all kinds of offers for both investments and financing. When we require a loan we seek the lowest possible interest rate but\u00a0 when we invest we want the highest rate of return. As we search for the best offer it is important to recognize that the advertised interest rate is not necessarily the true interest rate.\n\nAn advertised rate of 10% with annual<\/strong> compounding works out to be equivalent to a rate of 10% annually. We refer to this stated rate of 10% as the nominal<\/strong> interest rate.\u00a0 An advertised rate of 10% with daily<\/strong> compounding works out to be equivalent to a rate of 10.52%\u00a0 since interest is calculated on the interest 365 times in one year. We refer to the 10.52% as the effective<\/strong> interest rate.\n\nThe stated interest rate is referred to as the nominal interest rate<\/strong>, as it describes the named or numerical value. It is the rate that is usually stated in advertisements. The actual interest rate, or effective interest rate<\/strong>, reflects the real rate of return as it takes the compounding periods into account.\n\nWith simple interest calculations (where there is no compounding),\u00a0 the stated annual interest rate indicates the true rate of return. If $1000 is borrowed at 6% for one year, then the interest owined will be\u00a0 I = Prt = $1000 \u00d7 0.06\/yr \u00d7 1yr = $60.\n\nWith compound interest calculations,\u00a0 the stated annual interest rate does not indicate the true interest cost. If $1000 is invested at 6% for one year compounded semiannually, then the interest owed will be\u00a0 $60.90 rather than $60.\n\nOne way to determine the\u00a0 effective interest rat<\/strong>e is to divide the total compound interest for the first year by the principal amount. If in the first year $60.90 is the interest charged on a principal of $1000 then the effective interest rate is\u00a0 $60.90\/$1000 = 0.0609 = 6.09%.\u00a0 Although the nominal interest rate is 6%, the effective rate is 6.09%.\n\nIt is also possible to use a formula to calculate the effective interest rate.\n
\n Effective Interest Rate Formula<\/p>\n\n<\/header>\n
\n\nThe effective interest rate formula<\/strong> is:\n\n\n
\n [latex]f = \\left( 1 + \\frac{r}{n} \\right)^{n} - 1[\/latex]<\/td>\n where<\/td>\n f<\/em> = effective interest rate<\/td>\n<\/tr>\n \n <\/td>\n <\/td>\n r<\/em> = nominal interest rate (annual interest rate)<\/td>\n<\/tr>\n \n <\/td>\n <\/td>\n n<\/em> = number of times in one year that interest is calculated<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n \n EXAMPLE 1<\/p>\n\n<\/header>\n
\n\nUse the formula to determine the effective interest\u00a0 rate for 6% compounded annually.\n\nSolution<\/strong>\n\n\n
\n f<\/em> = ?\n\nr<\/em> = 6% = 0.06\n\nn<\/em> = 1<\/td>\n [latex]f = \\left( 1 + \\frac{r}{n} \\right)^{n} - 1[\/latex]<\/td>\n <\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1 + \\frac{0.06}{1} \\right)^{1} - 1[\/latex]<\/td>\n Replace the variables with their values<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1.06 \\right)^{1} - 1[\/latex]<\/td>\n Add [latex]1 + 0.06[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 1.06 - 1[\/latex]<\/td>\n <\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 0.06 = 6%[\/latex]<\/td>\n <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nThe effective interest rate is 6%. Note that the nominal and effective rate are the same since the number of compounding period is one (n = 1).\n\n<\/div>\n<\/div>\n \n TRY IT 1<\/p>\n\n<\/header>\n
\n\nWhat is the effective rate of 4% compounded yearly?\n\nShow answer<\/summary>4%\n\n<\/details><\/div>\n<\/div>\n
\n EXAMPLE 2<\/p>\n\n<\/header>\n
\n\nUse the formula to determine the effective interest\u00a0 rate for 6% compounded monthly.\n\nSolution<\/strong>\n\n\n
\n f<\/em> = ?\n\nr<\/em> = 6% = 0.06\n\nn<\/em> = 12<\/td>\n [latex]f = \\left( 1 + \\frac{r}{n} \\right)^{n} - 1[\/latex]<\/td>\n <\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1 + \\frac{0.06}{12} \\right)^{12} - 1[\/latex]<\/td>\n Replace the variables with their values<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1 + 0.005 \\right)^{12} - 1[\/latex]<\/td>\n Divide [latex]\\frac{0.06}{12}[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1.005 \\right)^{12} - 1[\/latex]<\/td>\n Add [latex]1 + 0.005[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 1.0617 - 1[\/latex]<\/td>\n Raise [latex]\\left( 1.005 \\right)^{12}[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 0.0617 = 6.17\\%[\/latex]<\/td>\n <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nThe effective interest rate is 6.17%\n\n<\/div>\n<\/div>\n \n TRY IT 2<\/p>\n\n<\/header>\n
\n\nWhat is the effective rate of 4% compounded monthly?\n\nShow answer<\/summary>4.07%\n\n<\/details><\/div>\n<\/div>\n
\n EXAMPLE 3<\/p>\n\n<\/header>\n
\n\nWhat is the effective rate for a nominal rate of 9.8% compounded weekly?\n\nSolution<\/strong>\n\n\n\n
\n f<\/em> = ?\n\nr<\/em> = 9.8% = 0.098\n\nn<\/em> = 52<\/td>\n [latex]f = \\left( 1 + \\frac{r}{n} \\right)^{n} - 1[\/latex]<\/td>\n <\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1 + \\frac{0.098}{52} \\right)^{52} - 1[\/latex]<\/td>\n Replace the variables with their values<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1 + 0.0018846 \\right)^{52} - 1[\/latex]<\/td>\n Divide [latex]\\frac{0.098}{52}[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1.0018846 \\right)^{52} - 1[\/latex]<\/td>\n Add [latex]1 + 0.0018846[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 1.102861 - 1[\/latex]<\/td>\n Raise [latex]\\left( 1.0018846 \\right)^{52}[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 0.102861 = 10.29\\%[\/latex]<\/td>\n \n\n <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\nThe effective interest rate is 10.29%\n\n<\/div>\n<\/div>\n \n TRY IT 3<\/p>\n\n<\/header>\n
\n\nDetermine the effective rate of interest on a loan that is advertised at a rate of 7.8% compounded daily.\n\nShow answer<\/summary>8.11%\n\n<\/details><\/div>\n<\/div>\nIt is important to consider the effective interest rate, rather than the nominal rate,\u00a0 when deciding on investments or loans.\n\nConsider Bank A which offers a savings plan at 6.25% compounded monthly and Bank B which offers 6.5% compounded semi-annually.\u00a0 Which of the two banks offers the better rate of return?\u00a0 Although both banks offer the same nominal interest rate, their effective rates differ.\u00a0 The effective rate will reflect the actual rate of return in one year. Example 4 will illustrate this.\n
\n EXAMPLE 4<\/p>\n\n<\/header>\n
\n\nBank A offers 6.25% compounded monthly while Bank B offers 6.5% compounded semi-annually.\u00a0 Which bank offers the better effective rate of return?\n\nSolution<\/strong>\n\nFor Bank A:\n\n\n
\n f<\/em> = ?\n\nr<\/em> = 6.25% = 0.0625\n\nn<\/em> = 12<\/td>\n [latex]f = \\left( 1 + \\frac{0.0625}{12} \\right)^{12} - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1 + 0.0052083 \\right)^{12} - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1.005208 \\right)^{12} - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 1.064322 - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 0.064322 = 6.43\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nFor Bank B:\n \n\n
\n f<\/em> = ?\n\nr<\/em> = 6.5% = 0.065\n n<\/em> = 2<\/p>\n<\/td>\n
[latex]f = \\left( 1 + \\frac{0.065}{2} \\right)^{2} - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1 + 0.0325 \\right)^{2} - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1.0325 \\right)^{2} - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 1.066056 - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 0.066056 = 6.61\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nNote that Bank A\u2019s effective rate, 6.43%, is less than both Bank B\u2019s nominal rate of 6.5% and Bank B\u2019s effective rate of 6.61%. Bank B offers the better effective rate of return.\n\n<\/div>\n<\/div>\n \n TRY IT 4<\/p>\n\n<\/header>\n
\n\nSam plans to invest a lottery win of\u00a0 $15,000. He is considering two different options. Option A offers 3.56% compounded weekly and Option B offers 3.48% componded monthly. Which option offers a better rate of return?\n\nShow answer<\/summary>Option A\u00a0 3.62%; Option B 3.54%;\u00a0 Option A offers a better rate of return.\n\n<\/details><\/div>\n<\/div>\n
\n EXAMPLE 5<\/p>\n\n<\/header>\n
\n\nConsider two options for a 2 year loan. Bank A will charge 7.2% compounded monthly while Bank B will charge 7.4% compounded semi-annually.\u00a0 Which bank offers the less expensive loan (charges the lower effective rate)?\n\nSolution<\/strong>\n\nFor Bank A:\n\n\n
\n f<\/em> = ?\n\nr<\/em> = 7.2% = 0.072\n\nn<\/em> = 12<\/td>\n [latex]f = \\left( 1 + \\frac{0.072}{12} \\right)^{12} - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1 + 0.006 \\right)^{12} - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1.006 \\right)^{12} - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 1.074424 - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 0.074424 = 7.44\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nFor Bank B:\n \n\n
\n f<\/em> = ?\n\nr<\/em> = 7.4% = 0.074\n\nn<\/em> = 2<\/td>\n [latex]f = \\left( 1 + \\frac{0.074}{2} \\right)^{2} - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1 + 0.037 \\right)^{2} - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = \\left( 1.037 \\right)^{2} - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 1.075369 - 1[\/latex]<\/td>\n<\/tr>\n \n <\/td>\n [latex]f = 0.075369 = 7.54\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nBank A\u2019s effective rate, 7.44%, is less than Bank B\u2019s effective rate of 7.54. By a slight margin, Bank A offers the less expensive loan.\n\n<\/div>\n<\/div>\n \n TRY IT 5<\/p>\n\n<\/header>\n
\n\nSam needs to borrow $5500. He is offered two different loans. One loan is\u00a0 at a bank for 6.8% compounded quarterly and the other is at a credit union for 6.9% compounded semiannually.\n\nWhich is the better option for Sam?\n\nShow answer<\/summary>Bank 6.98%; Credit Union 7.02%; the Bank is a slightly better option for a loan.\n\n<\/details><\/div>\n<\/div>\n
Key Concepts<\/h1>\n
- \n \t
- to determine the effective annual interest rate (f):\n
- \n \t
- [latex]f = \\left( 1 + \\frac{r}{n} \\right)^{n} - 1[\/latex]<\/li>\n<\/ul>\n<\/li>\n \t
- when investing money you want the higher effective interest rate; when borrowing money you want the lower effective interest rate.<\/li>\n<\/ul>\n
Glossary<\/strong><\/h1>\n
\n\neffective interest rate<\/strong>\n\ntakes the compounding periods into effect so it is a better reflection of the actual interest charges.\n\nnominal interest rate<\/strong>\n\nis normally the stated rate. It does not take the compounding periods into effect.\n\n<\/div>\n9.3 Exercise Set<\/h1>\n
- \n \t
- Determine the effective interest rates (rounded to two decimal places) for the following nominal interest rates when there is monthly compounding.\n
- \n \t
- 8%<\/li>\n \t
- 3.7%<\/li>\n \t
- 2.64%<\/li>\n \t
- 5%<\/li>\n<\/ol>\n<\/li>\n \t
- Determine the effective interest rates (rounded to two decimal places) for the following nominal interest rates when there is daily compounding.\n
- \n \t
- 8%<\/li>\n \t
- 3.7%<\/li>\n \t
- 2.64%<\/li>\n \t
- 5%<\/li>\n<\/ol>\n<\/li>\n \t
- Determine the effectiveinterest rate (rounded to two decimal places) when 10% is compounded\n
- \n \t
- Yearly<\/li>\n \t
- Semi-annually<\/li>\n \t
- Quarterly<\/li>\n \t
- Monthly<\/li>\n \t
- Weekly<\/li>\n \t
- Daily<\/li>\n<\/ol>\n<\/li>\n \t
- You have a choice between purchasing a savings certificate offering 3.6% simple interest or putting your money in a savings account at 3.6% compounded monthly. What is the difference between the effective\u00a0 rates?<\/li>\n \t
- What simple interest rate would give you the same return as\n
- \n \t
- 6% compounded daily?<\/li>\n \t
- 5% componded semiannually?<\/li>\n \t
- 4.2% componded weekly?<\/li>\n<\/ol>\n<\/li>\n \t
- \n
- \n \t
- What is the effective interest rate?<\/li>\n \t
- What total amount do you owe in four years?<\/li>\n \t
- What amount of this will be the interest charged?You borrow $4800 to be paid back in 4 years at a rate of 4.4% componded quarterly.<\/li>\n<\/ol>\n<\/li>\n \t
- You are needing to borrow $10,000 to be paid back over a 3 year period and you are consider two options. With Option A the interest rate is 3.5% compounded daily and with Option B the interest rate is 3.52% componded semiannually.\u00a0 Which option offers the less expensive loan (charges the lower effective rate)?<\/li>\n \t
- You invest $5600 for two years at a rate of 5.2% componded monthly.\n
- \n \t
- What is the effective interest rate?<\/li>\n \t
- What total amount will be in your account after two years?<\/li>\n \t
- What amount of this will be the interest earned?<\/li>\n<\/ol>\n<\/li>\n \t
- You can invest $2000 for one year under the following two options:\u00a0 Option A\u00a0 6.2 % simple interest or Option B\u00a0 6.15% compounded weekly.\u00a0 For each of these\n
- \n \t
- Determine the effective interest rate.<\/li>\n \t
- Determine the compound amount at the end of one year.<\/li>\n \t
- Determine the interest that is earned.<\/li>\n<\/ol>\n<\/li>\n \t
- L. Shark offers to lend you $1000 for one year at 50% interest compounded daily.\n
- \n \t
- What is the effective rate of interest on this loan (rounded to the nearest hundred<\/li>\n \t
- What total amount do you owe at the end of one year?<\/li>\n \t
- What is the interest component?<\/li>\n \t
- What would the interest component be if instead you were charged 50% simple interest?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n
Answers<\/h1>\n
- \n \t
- \n
- \n \t
- 8.30%<\/li>\n \t
- 3.76%<\/li>\n \t
- 2.67%<\/li>\n \t
- 5.12%<\/li>\n<\/ol>\n<\/li>\n \t
- \n
- \n \t
- 8.33%<\/li>\n \t
- 3.77%<\/li>\n \t
- 2.68%<\/li>\n \t
- 5.13%<\/li>\n<\/ol>\n<\/li>\n \t
- \n
- \n \t
- 10%<\/li>\n \t
- 10.25%<\/li>\n \t
- 10.38%<\/li>\n \t
- 10.47%<\/li>\n \t
- 10.51%<\/li>\n \t
- 10.52%<\/li>\n<\/ol>\n<\/li>\n \t
- The effective rate for 3.6% simple interest is 3.6%. The effective rate for 3.6% compounded monthly is 3.66%\u00a0 so a difference\u00a0 of\u00a0 0.06%.<\/li>\n \t
- \n
- \n \t
- 6.18%<\/li>\n \t
- 5.06%<\/li>\n \t
- 4.28%<\/li>\n<\/ol>\n<\/li>\n \t
- \n
- \n \t
- 4.47%<\/li>\n \t
- $5718.21<\/li>\n \t
- $918.21<\/li>\n<\/ol>\n<\/li>\n \t
- Option A the effective rate is 3.56%;\u00a0 Option B the effective rate is 3.55%. Option B is less expensive by 0.01%<\/li>\n \t
- \n
- \n \t
- 5.33%<\/li>\n \t
- $6212.37<\/li>\n \t
- $612.37<\/li>\n<\/ol>\n<\/li>\n \t
- \n
- \n \t
- Option A 6.2%\u00a0 and Option B\u00a0 6.34%<\/li>\n \t
- Option A\u00a0 $2124 and Option B\u00a0 $2126.78<\/li>\n \t
- Option A\u00a0 $124 and Option B\u00a0 $126.78<\/li>\n<\/ol>\n<\/li>\n \t
- \n
- \n \t
- 64.82%<\/li>\n \t
- $1648.16<\/li>\n \t
- $648.16<\/li>\n \t
- $500<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n
Attribution<\/h1>\nSome of the content for this chapter is from \"Unit 5: Nominal and effective rates of interest\" in Financial Mathematics<\/a> by Paul Grinder, Velma McKay, Kim Moshenko, and Ada Sarsiat, which is under a\u00a0CC BY 4.0 Licence<\/a>.. Adapted by Kim Moshenko. See the Copyright page for more information.<\/span>","rendered":"
![\"\"](\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2020\/06\/9.3-Intro-image-interest-1024x532.png\")
<\/p>\n\n\n Learning Objectives<\/p>\n<\/header>\n
\nBy the end of this section it is expected that you will be able to:<\/p>\n
- \n
- State the difference between nominal and effective interest rates<\/li>\n
- Determine the effective annual interest rate<\/li>\n
- Determine the best option when comparing nominal interest rates under different situations<\/li>\n<\/ul>\n<\/div>\n<\/div>\n
Nominal and Effective Rates of Interest<\/strong><\/h1>\n
As consumers and investors we are inundated with all kinds of offers for both investments and financing. When we require a loan we seek the lowest possible interest rate but\u00a0 when we invest we want the highest rate of return. As we search for the best offer it is important to recognize that the advertised interest rate is not necessarily the true interest rate.<\/p>\n
An advertised rate of 10% with annual<\/strong> compounding works out to be equivalent to a rate of 10% annually. We refer to this stated rate of 10% as the nominal<\/strong> interest rate.\u00a0 An advertised rate of 10% with daily<\/strong> compounding works out to be equivalent to a rate of 10.52%\u00a0 since interest is calculated on the interest 365 times in one year. We refer to the 10.52% as the effective<\/strong> interest rate.<\/p>\n
The stated interest rate is referred to as the nominal interest rate<\/strong>, as it describes the named or numerical value. It is the rate that is usually stated in advertisements. The actual interest rate, or effective interest rate<\/strong>, reflects the real rate of return as it takes the compounding periods into account.<\/p>\n
With simple interest calculations (where there is no compounding),\u00a0 the stated annual interest rate indicates the true rate of return. If $1000 is borrowed at 6% for one year, then the interest owined will be\u00a0 I = Prt = $1000 \u00d7 0.06\/yr \u00d7 1yr = $60.<\/p>\n
With compound interest calculations,\u00a0 the stated annual interest rate does not indicate the true interest cost. If $1000 is invested at 6% for one year compounded semiannually, then the interest owed will be\u00a0 $60.90 rather than $60.<\/p>\n
One way to determine the\u00a0 effective interest rat<\/strong>e is to divide the total compound interest for the first year by the principal amount. If in the first year $60.90 is the interest charged on a principal of $1000 then the effective interest rate is\u00a0 $60.90\/$1000 = 0.0609 = 6.09%.\u00a0 Although the nominal interest rate is 6%, the effective rate is 6.09%.<\/p>\n
It is also possible to use a formula to calculate the effective interest rate.<\/p>\n
\n\n Effective Interest Rate Formula<\/p>\n<\/header>\n
\nThe effective interest rate formula<\/strong> is:<\/p>\n
\n\n
\n ![\"f = \left( 1 + \frac{r}{n} \right)^{n} - 1\"](\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-297313c363c1ad528b36166981cac030_l3.png\" "\\"Rendered")
<\/td>\nwhere<\/td>\n f<\/em> = effective interest rate<\/td>\n<\/tr>\n \n <\/td>\n <\/td>\n r<\/em> = nominal interest rate (annual interest rate)<\/td>\n<\/tr>\n \n <\/td>\n <\/td>\n n<\/em> = number of times in one year that interest is calculated<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n \n\n EXAMPLE 1<\/p>\n<\/header>\n
\nUse the formula to determine the effective interest\u00a0 rate for 6% compounded annually.<\/p>\n
Solution<\/strong><\/p>\n
\n\n
\n f<\/em> = ?<\/p>\n r<\/em> = 6% = 0.06<\/p>\n
n<\/em> = 1<\/td>\n
<\/td>\n<\/td>\n<\/tr>\n \n <\/td>\n ![\"f = \left( 1 + \frac{0.06}{1} \right)^{1} - 1\"](\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-873bd8b8799b976f081347b40d858b8d_l3.png\" "\\"Rendered")
<\/td>\nReplace the variables with their values<\/td>\n<\/tr>\n \n <\/td>\n ![\"f = \left( 1.06 \right)^{1} - 1\"](\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9d2938fb824fe8b0ef9c1e00d82d6163_l3.png\" "\\"Rendered")
<\/td>\nAdd ![\"1 + 0.06\"](\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0b64336d8c39bdd8139934ab744b1160_l3.png\" "\\"Rendered")
<\/td>\n<\/tr>\n\n <\/td>\n ![\"f = 1.06 - 1\"](\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-76df8b0ee2986aafe8261575310fcade_l3.png\" "\\"Rendered")
<\/td>\n<\/td>\n<\/tr>\n \n <\/td>\n ![\"f = 0.06 = 6%\"](\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-82144d185c10f217dd6dfd98f6acc1c2_l3.png\" "\\"Rendered")
<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n The effective interest rate is 6%. Note that the nominal and effective rate are the same since the number of compounding period is one (n = 1).<\/p>\n<\/div>\n<\/div>\n
\n\n TRY IT 1<\/p>\n<\/header>\n
\nWhat is the effective rate of 4% compounded yearly?<\/p>\n
\nShow answer<\/summary>\n
4%<\/p>\n<\/details>\n<\/div>\n<\/div>\n
\n\n EXAMPLE 2<\/p>\n<\/header>\n
\nUse the formula to determine the effective interest\u00a0 rate for 6% compounded monthly.<\/p>\n
Solution<\/strong><\/p>\n
\n\n
\n
- \n
- Determine the effective interest rates (rounded to two decimal places) for the following nominal interest rates when there is monthly compounding.\n
- to determine the effective annual interest rate (f):\n