What amount is to be repaid on a loan of 10000 for 1 and half years at 10% per annum compounded half yearly?

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

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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`