 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Anur followed money to be repaid in 50 months with interest of $3,980. If he repaid the loan after 35 months, then how much interest rebate did he get? To find the interest rebate we follow the below steps. The first step is to calculate refund fraction or rebate fraction using rule of 78. Rebate fraction is equal to sum of digits for number of payments remaining upon sum of digits for total number of payments. Next step is to find the interest rebate using the formula. Interest rebate is equal to total interest into rebate fraction. With this key idea let us proceed with the solution. In this question we are given that Anur borrowed money to be repaid in 50 months. The interest of his loan is $3,980. This loan is repaid early in 35 months. We have to calculate the interest rebate. So now using the key idea we first find the rebate fraction. We know that rebate fraction is equal to sum of digits for number of payments remaining upon sum of digits for total number of payments. So here the loan is repaid in 35 months. This implies number of payments remaining is equal to 15 minus 35 equal to 15. That means 15 monthly payments are remaining. Total number of payments is equal to 50. This implies rebate fraction is equal to sum of digits for number of payments remaining that is 1 plus 2 plus 3 plus 4 plus so on plus 15 upon sum of digits for total number of payments that is 1 plus 2 plus 3 plus 4 plus so on plus 50. So now we know if n is very large then sum of digits is equal to n into n plus 1 by 2. So here n is equal to 15 in the numerator and n is equal to 50 in the denominator. This implies sum of digits in the numerator will be 15 into 15 plus 1 upon 2 and the sum of digits in the denominator will be 50 into 50 plus 1 upon 2. So the rebate fraction is equal to 15 into 15 plus 1 upon 2 the whole upon 50 into 50 plus 1 upon 2. 2 and 2 cancels this becomes equal to 15 into 16 upon 50 into 51. 2 into 8 is 16 and 2 into 25 is 50. 5 threes are 15 and 5 fives are 25. 3 into 17 is 51. So this is equal to 8 upon 85. That means rebate fraction is equal to 8 upon 85. Now our next step is to calculate the interest rebate. We know interest rebate is equal to total interest into rebate fraction. So interest rebate is equal to $3980 into 8 upon 85 which is equal to $374.58. So Arnold will get the interest rebate of $374.58 which is a required answer. This completes our session. Hope you enjoyed this session.