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» We provide you study material i.e. PDF's for offline use. Example: What is the nominal rate of interest on a company that has a 7.77% rate of effective interest annually (rounded to two decimal places)? Solution: Since we're looking for the nominal rate of interest, we are determining \(j\). First, we can identify the information that is given in the problem: \(m = 12\) (months per year), \(i=7.77\%=0.0777\) We can use the effective interest rate formula, \(i=(1+\frac{j}{m})^m-1\), substitute the above values and solve for \(r\): \(0.0777=(1+\frac{j}{12})^{12}-1\) \(0.0777+1=(1+\frac{j}{12})^{12}\) \(\sqrt[12]{1.0777}-1=\frac{j}{12}\) \(j=12(\sqrt[12]{1.0777}-1) \approx 0.0751\) So, the nominal rate of interest on a company that has a 7.77% effective rate (compounded annually per year) is \(7.51\%\) compounded monthly per year. Example: A credit card company charges 21% interest per year, compounded monthly. What effective annual interest rate (to two decimal places) does the company charge? Solution: Since we're looking for the effective rate, we are determining \(f\). First, we can identify the information that is given in the problem: \(m = 12\) (months per year), \(j=21\%=0.21\) We can use the effective interest rate formula, \(i=(1+i)^m-1\), substitute the above values and solve for \(f\): \(f=(1+\frac{0.21}{12})^{12}-1\) \(f=(1+0.0175)^{12}-1\) \(f \approx 0.2314\) So, effective rate the company charges is \(23.14\%\) compounded annually per year.
4. Relationship between annual nominal rate of interest and annual effective rate of interest, iffrequency of compounding is greater than one:a) Effective rate > Nominal rateb) Effective rate < Nominal ratec) Effective rate = Nominal rated) None of the aboveAnswer:a 5. Mr. X takes a loan of Rs 50,000 from HDFC Bank. The rate of interest is 10% per annum. The firstinstallment will be paid at the end of year 5. Determine the amount of equal annual installments if Mr. Xwishes to repay the amount in five installments. Get answer to your question and much more We have textbook solutions for you! The document you are viewing contains questions related to this textbook. Finite Mathematics for the Managerial, Life, and Social Sciences: An Applied Approach Tan Expert Verified 6. If nominal rate of return is 10% per annum and annual effective rate of interest is 10.25% per annum,determine the frequency of compounding: Get answer to your question and much more 7. Present value tables for annuity cannot be straight away applied to varied stream of cash flows. Get answer to your question and much more 8. Heterogeneous cash flows can be made comparable bya) Discounting techniqueb) Compounding techniquec) Either a or bd) None of the aboveAnswer:c 9. Value which converts series of equal payments in to value received at beginning of investment isclassified as Get answer to your question and much more 10.Value which converts series of equal payments in to value received at end time of investment isclassified as Get answer to your question and much more End of preview. Want to read all 4 pages? Upload your study docs or become a Course Hero member to access this document We have textbook solutions for you!The document you are viewing contains questions related to this textbook. The document you are viewing contains questions related to this textbook. Finite Mathematics for the Managerial, Life, and Social Sciences: An Applied Approach Tan Expert Verified What is the relationship between annual nominal rate of interest and annual effective rate of interest if frequency of compounding is greater than one?In this case, the nominal annual interest rate is 10%, and the effective annual interest rate is also 10%. However, if compounding is more frequent than once per year, then the effective interest rate will be greater than 10%. The more often compounding occurs, the higher the effective interest rate.
What is the relationship between nominal interest rate and real or effective interest rate?A nominal interest rate refers to the total of the real interest rate plus a projected rate of inflation. A real interest rate provides the actual return on a loan (to the lender) and on a bond (to the investor).
What is the relationship between the nominal interest rate and the annual percentage?The nominal interest rate, also known as an Annualised Percentage Rate or APR, is the periodic interest rate multiplied by the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded).
Is effective rate the same as nominal rate compounded annually?The effective annual rate is normally higher than the nominal rate because the nominal rate quotes a yearly percentage rate regardless of compounding. Increasing the number of compounding periods increases the effective annual rate as compared to the nominal rate.
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Relationship between annual nominal rate of interest and annual effective rate of interest
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