A man borrows rs. 20,000 at 10% compound interest. at the end of every year he pays rs. 2000 as part repayment. how much does he still owe after three such installments?
Answers
Amount to be paid after three years on compound interest is 20,000 * (1+10/100) ^ 3
Thus, after three years, he has to pay Rs 26,620 (i).
But, after first year he has cleared Rs. 2,000. So, only compound interest for two years remain. The first year deduction has to be made along with its compound interest.
Thus, the amount to be paid is 26,620 - 2,000 – 2,000 * (1 + 10/100) ^ 2 = 26,620 – 2,000 * (1 + 10/100) ^ 2 (ii)
Again, when he repays 2,000 after two years, the due amount is the amount in Eqn (ii) - 2,000 and its compound interest for one year.
So, now the amount to be paid is 26,620 - 2,000 * (1 + 10/100) ^ 2 - 2,000 - 2,000 * (1 + 10/100) ^ 1 =
26,620 - 2,000 * (1 + 10/100) ^ 2 - 2,000 * (1 + 10/100) ^ 1 (iii)
Once more, he pays 2,000 after the third year. So, this amount has to be deducted from the above.
Thus, the final amount to be repaid is 26,620 - 2,000 * (1 + 10/100) ^ 2 - 2,000 * (1 + 10/100) ^ 1 - 2,000
In other words, the final repayable amount is 26,620 - 2,000 *[ (1 + 10/100 ^ 2) + (1 + 10/100) + 1]
Therefore total amount pending for repayment after three years is 26,620 – 2,000 *[ 1.1 ^ 2 + 1.1 + 1] = 26,620 - 6,620 = Rs. 20,000
Answer:
14320
Step-by-step explanation:
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