Solution: 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:
100 Questions 100 Marks 60 Mins
Given: The sum = Rs 12,000 Time = \(1 \frac{1}{2}\) years Rate = 10% p.a. Formula used: A = P(1 + R/100)t Here, A, P, R and t are the Amount, Principal, Rate and time respectively Concept used: When compounded half-yearly then, Rate is half and time is doubled Calculation: Rate = 10%/2 = 5% and Time = \(1 \frac{1}{2}\) × 2 = 3 half yearly Now, A = P(1 + R/100)t ⇒ A = 12000(1 + 5/100)3 ⇒ A = 12000 × 21/20 × 21/20 × 21/20 ⇒ A = 13891.5 ∴ The total amounts to be paid is Rs 13891.50 India’s #1 Learning Platform Start Complete Exam Preparation
Daily Live MasterClasses
Practice Question Bank
Mock Tests & Quizzes Trusted by 3.3 Crore+ Students
Last updated at Nov. 12, 2018 by Teachoo
Support Teachoo in making more (and better content) - Monthly, 6 monthly, yearly packs available! |