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Rahul takes a loan of Rs.3.2 lakhs for his business for a period of 2 years. He wishes to pay the amount in 2 equal instalments, at the end of the first year and at the end of the second year. The future value of both the instalments combined, at the end of the second year is Rs.5 lacs. What approximate percentage of amount did he save while paying in instalments as compared to the condition where he would have paid all the amount at the end of 2 years.

Question

Rahul takes a loan of Rs.3.2 lakhs for his business for a period of 2 years. He wishes to pay the amount in 2 equal instalments, at the end of the first year and at the end of the second year. The future value of both the instalments combined, at the end of the second year is Rs.5 lacs. What approximate percentage of amount did he save while paying in instalments as compared to the condition where he would have paid all the amount at the end of 2 years.

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Solution

To solve this problem, we first need to understand the scenario. Rahul takes a loan of Rs. 3.2 lakhs and pays it back in two equal instalments over two years. The combined future value of these instalments at the end of the second year is Rs. 5 lakhs.

Step 1: Calculate the amount of each instalment. Since the instalments are equal, each one would be half of the total future value, which is Rs. 5 lakhs. So, each instalment is Rs. 5 lakhs / 2 = Rs. 2.5 lakhs.

Step 2: Calculate the total amount Rahul would have paid if he had paid the entire amount at the end of two years. This would be the original loan amount, which is Rs. 3.2 lakhs.

Step 3: Calculate the difference between the total amount Rahul would have paid at the end of two years and the total amount he actually paid in instalments. This is Rs. 3.2 lakhs - Rs. 2.5 lakhs = Rs. 0.7 lakhs.

Step 4: Calculate the percentage of the amount Rahul saved by paying in instalments. This is the difference calculated in step 3 divided by the total amount he would have paid at the end of two years, multiplied by 100. So, the percentage saved is (Rs. 0.7 lakhs / Rs. 3.2 lakhs) * 100 = 21.875%.

So, Rahul saved approximately 22% by paying in instalments compared to if he had paid the entire amount at the end of two years.

This problem has been solved

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