For example, a loan with 10 percent interest compounded monthly will actually carry an interest rate higher than 10 percent, because more interest is accumulated each month. The effective interest rate calculation does not take into account one-time fees like loan origination fees. These fees are considered, however, in the calculation of the annual percentage rate.
The stated interest rate is usually the “headline” interest rate. It’s the number that the lender typically advertises as the interest rate.
Usually, the compounding period is monthly. You’ll still want to check with your lender to verify that, though.
In this formula, r represents the effective interest rate, i represents the stated interest rate, and n represents the number of compounding periods per year.
After familiarising the theory, do the maths differently. Find the number of intervals for a year. It is 2 for semi-annual, 4 for quarterly, 12 for monthly, 365 for daily. Number of intervals per year x 100 plus the interest rate. If the interest rate is 5%, it is 205 for semi-annual, 405 for quarterly, 1205 for monthly, 36505 for daily compounding. Effective interest is the value in excess of 100, when the principal is 100. Do the maths as: ((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 The value exceeding 100 in case ‘a’ is the effective interest rate when compounding is semi-annual. Hence 5. 063 is the effective interest rate for semi-annual, 5. 094 for quarterly, 5. 116 for monthly, and 5. 127 for daily compounding. Just memorise in the form of a theorem. (No of intervals x 100 plus interest )divided by (number of intervals x100) raised to the power of intervals, the result multiplied by 100. The value exceeding 100 will be the effective interest yield.
