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What is known: Principal, Time Period, and Rate of Interest What is unknown: Amount and Compound Interest (C.I.) Reasoning: A = P[1 + (r/100)]n P = ₹ 10,000 n = \(1{\Large\frac{1}{2}}\) years R = 10% p.a. compounded annually and half-yearly where , A = Amount, P = Principal, n = Time period and R = Rate percent For calculation of C.I. compounded half-yearly, we will take the Interest rate as 5% and n = 3 A = P[1 + (r/100)]n A = 10000[1 + (5/100)]3 A = 10000[1 + (1/20)]3 A = 10000 × (21/20)3 A = 10000 × (21/20) × (21/20) × (21/20) A = 10000 × (9261/8000) A = 5 × (9261/4) A = 11576.25 Interest earned at 10% p.a. compounded half-yearly = A - P = ₹ 11576.25 - ₹ 10000 = ₹ 1576.25 Now, let's find the interest when compounded annually at the same rate of interest. Hence, for 1 year R = 10% and n = 1 A = P[1 + (r/100)]n A = 10000[1 + (10/100)]1 A = 10000[1 + (1/10)] A = 10000 × (11/10) A = 11000 Now, for the remaining 1/2 year P = 11000, R = 5% A = P[1 + (r/100)]n A = 11000[1 + (5/100)] A = 11000[(105/100)] A = 11000 × 1.05 A = 11550 Thus, amount at the end of \(1{\Large\frac{1}{2}}\)when compounded annually = ₹ 11550 Thus, compound interest = ₹ 11550 - ₹ 10000 = ₹ 1550 Therefore, the interest will be less when compounded annually at the same rate. ☛ Check: NCERT Solutions for Class 8 Maths Chapter 8 Video Solution: Find the amount and the compound interest on ₹ 10,000 for \(1{\Large\frac{1}{2}}\) years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?NCERT Solutions Class 8 Maths Chapter 8 Exercise 8.3 Question 8 Summary: The amount and the compound interest on ₹ 10,000 for \(1{\Large\frac{1}{2}}\) years at 10% per annum, compounded half-yearly is ₹ 11576.25 and ₹ 1576.25 respectively. The interest will be less when compounded annually at the same rate. ☛ Related Questions:
Zigya App Here P = Rs 10000, T = 1 year R = 8% p.a. compounded half yearly. ∴ R = 8% p.a. = 4% half yearly T = 1 year n = 2 1 = 2Now, amount = = Rs 10,000 = Rs 10,000 = Rs 10,000 = Rs CI = 10816 - 10000 = Rs 816 80 Views Comparing QuantitiesHope you found this question and answer to be good. Find many more questions on Comparing Quantities with answers for your assignments and practice. Explore. Zig In MathematicsBrowse through more topics from Mathematics for questions and snapshot. Explore. Zig In What will be the compound interest on rupees 10000 for 1 year at 8% per annum if the interest is compounded half yearly?(10816 - 10000) = Rs. 816.
What is the amount on ₹ 10000 for 1 year at 8 per annum compounded half yearly?Thus, C.I. = A.P = Rs 1,248.64. Q.
What is the interest of 10000 of 8%?20280 at the end of one year, when the interest is compounded half yearly.
What is compound interest on an amount of Rs 10000 at 8% per annum for 2 years?Solution. ∴ Compound interest is ₹ 1698.58.
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