Effective rate of interest
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The effective rate of interest is the actual rate earned or paid on an investment when interest is compounded over time. It is usually higher than the nominal rate. The effective rate depends on both the nominal rate and the number of compounding periods. More compounding periods result in a higher effective rate. In the example given, a 6% nominal interest rate compounded semi-annually yields an effective rate of 6.09%, compounded quarterly yields 6.14%, and compounded monthly yields the highest rate of 6.17%.
Effective rate of interest
- 1. NADEEM UDDIN ASSOCIATE PROFESSOR OF STATISTICS https://www.slideshare.net/NadeemUddin17 https://nadeemstats.wordpress.com/listofbooks/
- 2. Effective Rate of Interest: The Effective Rate of interest is the rate of interest actually earned on an investment or paid on a loan as a result of compounding the interest over a given period of time. It is usually higher than the nominal rate and is used to compare different financial products that calculate annual interest with different compounding periods – weekly, monthly, quarterly, semi annually, and yearly. Increasing the number of compounding periods makes the effective interest rate increase as time goes by.
- 3. Formula for Effective Rate of Interest: Effective Rate of Interset = 1 + nominal interest rate number of compounding periods number of compounding periods − 1 𝐄𝐟𝐟𝐞𝐜𝐭𝐢𝐯𝐞 𝐑𝐚𝐭𝐞 𝐨𝐟 𝐈𝐧𝐭𝐞𝐫𝐬𝐞𝐭 = 𝟏 + 𝒊 𝒎 𝒎 − 𝟏 OR i = 𝐧𝐨𝐦𝐢𝐧𝐚𝐥 𝐢𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐫𝐚𝐭𝐞 m = 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐜𝐨𝐦𝐩𝐨𝐮𝐧𝐝𝐢𝐧𝐠 𝐩𝐞𝐫𝐢𝐨𝐝𝐬 Where
- 4. Nominal Rate of Interest: A nominal rate interest is a stated rate indicated by a financial instrument that is issued by a lender or guarantor. This rate is the basis for computation to derive the interest amount resulting from compounding the principal plus interest over a period of time. This is the actual monetary price that borrowers pay to lenders or that investors receive from issuers.
- 5. Compounding Period: A compounding period is the time period after which the outstanding loan or investment’s interest is added to the principal amount of said loan or investment. The period can be daily, weekly, monthly, quarterly, or semi-annually, depending on the terms agreed upon by the parties involved. As the number of compounding periods increases so does the amount of interest earned or paid on the money used. Quarterly compounding produces higher returns than semi-annual compounding, while monthly compounding generates more than quarterly, and daily compounding generates more than monthly.
- 6. Example-1 Find the effective rate of interest a) 6% compounded semi-annually. b) 6% compounded quarterly. c) 6% compounded monthly. Solution: (a) m e 2 e i 6% 6 0.06 100 m 2 we know that i r (1 ) 1 m 0.06 r (1 ) 1 2
- 7. 2 e e e e r (1 0.03) 1 r 1.0609 1 r 0.609 r 6.09% (b) m 4 e 4 4 e e i 6% 6 0.06 100 m 4 we know that i 0.06 r (1 ) 1 (1 ) 1 m 4 r (1 0.015) 1 (1.015) 1 r 1.0614 1 0.0614 6.14%
- 8. (c) m 12 e i 6% 6 0.06 100 m 12 we know that i 0.06 r (1 ) 1 (1 ) 1 m 12 12 12 e e r (1 0.005) 1 (1.005) 1 r 1.0617 1 0.0617 6.17% Comments 𝐜𝐨𝐦𝐩𝐨𝐮𝐧𝐝𝐞𝐝 𝒔𝒆𝒎𝒊 − 𝐚𝐧𝐧𝐮𝐚𝐥𝐥𝐲 ˂ 𝐜𝐨𝐦𝐩𝐨𝐮𝐧𝐝𝐞𝐝 𝐪𝐮𝐚𝐫𝐭𝐞𝐫𝐥𝐲 ˂ 𝐜𝐨𝐦𝐩𝐨𝐮𝐧𝐝𝐞𝐝 𝐦𝐨𝐧𝐭𝐡𝐥𝐲 𝟔. 𝟎𝟗% < 𝟔. 𝟏𝟒% < 𝟔. 𝟏𝟕%