Verified by Ajay Kumar
A loan of ₹12,400 is taken at 10% compound interest, payable in two equal annual installments. Find the approximate installment amount.
₹7,643
₹7,043
₹7,743
₹7,145
Answer: D
Solution: Let each annual installment be x. Discounting both installments to the present, \(\frac{x}{1.1}+\frac{x}{1.1^2}=12400\). Therefore, \(x\left(\frac{1}{1.1}+\frac{1}{1.21}\right)=12400\), which gives \(x\approx7145\). The approximate installment is ₹7,145. Trick: Bring each future installment to present value using the compound-interest discount factor.
10% चक्रवृद्धि ब्याज पर ₹12,400 का ऋण लिया जाता है, जिसे दो समान वार्षिक किस्तों में चुकाना है। प्रत्येक किस्त की अनुमानित राशि ज्ञात कीजिए।
₹7,643
₹7,043
₹7,743
₹7,145
उत्तर: D
हल: प्रत्येक वार्षिक किस्त x मानें। दोनों किस्तों का वर्तमान मूल्य लेने पर \(\frac{x}{1.1}+\frac{x}{1.1^2}=12400\)। इसलिए \(x\left(\frac{1}{1.1}+\frac{1}{1.21}\right)=12400\), जिससे \(x\approx7145\) मिलता है। अनुमानित किस्त ₹7,145 है। ट्रिक: चक्रवृद्धि ब्याज के छूट गुणक का प्रयोग करके प्रत्येक भविष्य की किस्त का वर्तमान मूल्य निकालें।
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