We will learn how to use the formula for calculating the compound interest when interest is compounded half-yearly. Show Computation of compound interest by using growing principal becomes lengthy and complicated when the period is long. If the rate of interest is annual and the interest is compounded half-yearly (i.e., 6 months or, 2 times in a year) then the number of years (n) is doubled (i.e., made 2n) and the rate of annual interest (r) is halved (i.e., made \(\frac{r}{2}\)). In such cases we use the following formula for compound interest when the interest is calculated half-yearly. If the principal = P, rate of interest per unit time = \(\frac{r}{2}\)%, number of units of time = 2n, the amount = A and the compound interest = CI Then A = P(1 + \(\frac{\frac{r}{2}}{100}\))\(^{2n}\) Here, the rate percent is divided by 2 and the number of years is multiplied by 2 Therefore, CI = A - P = P{(1 + \(\frac{\frac{r}{2}}{100}\))\(^{2n}\) - 1} Note: A = P(1 + \(\frac{\frac{r}{2}}{100}\))\(^{2n}\) is the relation among the four quantities P, r, n and A. Given any three of these, the fourth can be found from this formula. CI = A - P = P{(1 + \(\frac{\frac{r}{2}}{100}\))\(^{2n}\) - 1} is the relation among the four quantities P, r, n and CI. Given any three of these, the fourth can be found from this formula. Word problems on compound interest when interest is compounded half-yearly: 1. Find the amount and the compound interest on $ 8,000 at 10 % per annum for 1\(\frac{1}{2}\) years if the interest is compounded half-yearly. Solution: Here, the interest is compounded half-yearly. So, Principal (P) = $ 8,000 Number of years (n) = 1\(\frac{1}{2}\) × 2 = \(\frac{3}{2}\) × 2 = 3 Rate of interest compounded half-yearly (r) = \(\frac{10}{2}\)% = 5% Now, A = P (1 + \(\frac{r}{100}\))\(^{n}\) ⟹ A = $ 8,000(1 + \(\frac{5}{100}\))\(^{3}\) ⟹ A = $ 8,000(1 + \(\frac{1}{20}\))\(^{3}\) ⟹ A = $ 8,000 × (\(\frac{21}{20}\))\(^{3}\) ⟹ A = $ 8,000 × \(\frac{9261}{8000}\) ⟹ A = $ 9,261 and Compound interest = Amount - Principal = $ 9,261 - $ 8,000 = $ 1,261 Therefore, the amount is $ 9,261 and the compound interest is $ 1,261 2. Find the amount and the compound interest on $ 4,000 is 1\(\frac{1}{2}\) years at 10 % per annum compounded half-yearly. Solution: Here, the interest is compounded half-yearly. So, Principal (P) = $ 4,000 Number of years (n) = 1\(\frac{1}{2}\) × 2 = \(\frac{3}{2}\) × 2 = 3 Rate of interest compounded half-yearly (r) = \(\frac{10}{2}\)% = 5% Now, A = P (1 + \(\frac{r}{100}\))\(^{n}\) ⟹ A = $ 4,000(1 + \(\frac{5}{100}\))\(^{3}\) ⟹ A = $ 4,000(1 + \(\frac{1}{20}\))\(^{3}\) ⟹ A = $ 4,000 × (\(\frac{21}{20}\))\(^{3}\) ⟹ A = $ 4,000 × \(\frac{9261}{8000}\) ⟹ A = $ 4,630.50 and Compound interest = Amount - Principal = $ 4,630.50 - $ 4,000 = $ 630.50 Therefore, the amount is $ 4,630.50 and the compound interest is $ 630.50 ● Compound Interest Compound Interest Compound Interest with Growing Principal Compound Interest with Periodic Deductions Compound Interest by Using Formula Compound Interest when Interest is Compounded Yearly Problems on Compound Interest Variable Rate of Compound Interest Practice Test on Compound Interest ● Compound Interest - Worksheet Worksheet on Compound Interest Worksheet on Compound Interest with Growing Principal Worksheet on Compound Interest with Periodic Deductions Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need. What is the difference between the compound interest compounded yearly and half yearly for 18 months?∴ The difference between the compound interest compounded yearly and compounded half yearly for 18 months at 20% per annum on a sum of Rs. 12,000 is Rs. 132.
What is the difference between the compound interest compounded annually?The difference between simple and compound interest compounded annually on a certain sum of money for 2 years at 4% per annum is ₹1.
What does compounding half yearly mean?If the time period for the calculation of interest is half-yearly, the interest is calculated every six months, and the amount is compounded twice a year. The compound interest half-yearly formula makes the number of years double and the rate of interest is made into half.
What is the difference between compounded annually and compounded monthly?Examples: "12% interest" means that the interest rate is 12% per year, compounded annually. "12% interest compounded monthly" means that the interest rate is 12% per year (not 12% per month), compounded monthly. Thus, the interest rate is 1% (12% / 12) per month.
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