what will be the effective rate of interest for the first year. if the rate of interest is 40% p.a.compunded semi annual.. with formula I need.
Answers
Answer:
By now, you have a clear understanding of simple and compound interest. However, when interest is compounded, for more than one year, the actual interest rate per annum is lesser than the effective rate of interest. In this article, we will look at the definition, formula, and some examples of calculating the effective rate of interest.
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Effective Rate of Interest
effective rate of interestSource: Pixabay
Definition
The effective rate of interest is the equivalent annual rate of interest which is compounded annually. Further, the compounding must happen more than once every year. Let’s look at an example for better clarity:
Example 1: Peter invests Rs. 10,000 for one year at the rate of 6% per annum. The interest is compounded semi-annually. Let’s calculate the interest earned in the first six months (I1).
Solution: I1 = 10,000 x 6100 x 612 = Rs. 300. Since the interest is compounded, the principal for the next 6 months = 10,000 + 300 = Rs. 10,300. Therefore, the interest earned in the next six months (I2) is,
I2 = 10,300 x \( \frac {6}{100} \) x 612 $$ = Rs. 309.
Hence, the total interest earned during the year I = I1 + I2 = 300 + 309 = Rs. 609. We know the formula for interest is I = PNR … where ‘I’ is the interest, ‘P’ is the principal amount, ‘N’ is the time period, and ‘R’ is the rate of interest. In the case of this example, R = E or the effective rate of interest. Therefore, we have,
E = IPN = 60910,000×1 = 0.0609 or 6.09%.