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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
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Calculate the amount and compound interest on: (a) Rs 10,800 for 3 years at 121/2 % per annum compounded annually. (b) Rs 18,000 for 21/2 years at 10% per annum compounded annually. (c) Rs 62,500 for 11/2 years at 8% per annum compounded half yearly (d) Rs 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify.) (e) Rs 10,000 for 1 year at 8% per annum compounded half yearly.
Text Solution Solution : Here, interest is compounded half-yearly.So, <br> Time, `t = 3` half years<br> `:.`Rate of interest `r = 10/2 = 5% ` per half yearly<br> Loan amount, `P = "Rs." 12000` <br> So, Amount to be repaid, `A = 12000(1+5/100)^3`<br> `A = 12000xx(21/20)xx(21/20)xx(21/20) = "Rs."13891.5`
Last updated at Nov. 12, 2018 by Teachoo
Example 12 What amount is to be repaid on a loan of Rs 12000 for 1 1/2 years at 10% per annum compounded half yearly. Given Principal = Rs 12000 Here, rate is compounded half yearly. Rate of interest = R = 10/2 % = 5 % & Time = 1 1/2 years = 3/2 years = 3/2 × 2 half years = 3 Amount = P (1+𝑅/100)^𝑛 = 12000 (1+5/100)^3 = 12000 (1+1/20)^3 = 12000 ((20 + 1)/20)^3 = 12000 (21/20)^3 = 12000 × 21/20 × 21/20 × 21/20 = 12 × 21/2 × 21/2 × 21/2 = 3 × 21 × 21 × 21/2 = (63 × 441)/2 = 27783/2 = 13891.5 ∴ Amount = Rs 13,891.50 |