Why we double the time in a compound interest when compounded half yearly?
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The formula for compounding is A=P(1+r/100)^n. Now, what does the formula mean, simply put every year the money you had earlier put (principal) would be multiplied by a factor ( 1+r/100) a certain number of times (years you invested/loaned) ,right?
Now if you start compounding half yearly, what would change? Say you were getting Rs 10 on Rs 100 for an year i.e. 10% interest, now the person would give you only Rs 5 as you have invested for half year right? So, you can say the ROI for half year is half of that of full year. Now, after half an year your money has amounted to Rs 105, now for the course of next half year this would act as your principal? That is why, now the number of times your money would be multiplied would be doubled, as the amount is compounded twice instead of once every year. If you understand this basic you won’t have to mug up the formula. Now, if you are given compounded thrice the ROI would be 1/3rd and number of times it is multiplied would be tripled.
Now if you start compounding half yearly, what would change? Say you were getting Rs 10 on Rs 100 for an year i.e. 10% interest, now the person would give you only Rs 5 as you have invested for half year right? So, you can say the ROI for half year is half of that of full year. Now, after half an year your money has amounted to Rs 105, now for the course of next half year this would act as your principal? That is why, now the number of times your money would be multiplied would be doubled, as the amount is compounded twice instead of once every year. If you understand this basic you won’t have to mug up the formula. Now, if you are given compounded thrice the ROI would be 1/3rd and number of times it is multiplied would be tripled.
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