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The cash price of a refrigerator is Rs. 7044. A customer paid Rs. 2000 in case and promised to pay the remaining money in 3 yearly equal instalments at the rate of 5% per annum compound interest. What is the value of each instalment ?
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- Rs. 1865
- Rs. 1868.28
- Rs. 1752
- Rs. 1852.20
Correct Option: D
Remaining money = 7044 - 2000 = Rs. 5044
If each installment is of Rs. P
When the amount is Rs. P at the end of first, second and third year at the rate of 5% then principal will be - P/(1 + 5/100), P/(1 +5/100)2 and P/(1 +5/100)3
∴ P/(1 +5/100) + P/(1 + 5/100)2 + P/(1 +5/100)3 = 5044
⇒ P(20/21) + P(20/21)2 + P(20/21)3 = 5044
⇒ P(20/21) { 1 +(20/21) + (20/21)2} = 5044
⇒ P(20/21) {1 +20/21 +400/441} = 5044
⇒ P(20/21) {441 + 420 + 400/441} =5044
⇒ P(20/21) (1261/441) =5044
∴ P = (5044 x 21 x 441)/ (20 x 1261) = Rs. 1852.20
