Verified by Ajay Kumar
A sum of ₹20,000 is borrowed at 10% compound interest, to be repaid in two equal annual installments. Find the approximate value of each installment.
₹11,922
₹12,522
₹11,524
₹11,022
Answer: C
Solution: Let each annual installment be x. Taking the present value of both installments, \(\frac{x}{1.1}+\frac{x}{1.1^2}=20000\). Thus, \(x(0.90909+0.82645)=20000\), giving \(x\approx11523.81\). Therefore, each installment is approximately ₹11,524. Trick: Discount each future installment to the present using the compound-interest factor.
₹20,000 की राशि 10% चक्रवृद्धि ब्याज पर उधार ली जाती है और इसे दो समान वार्षिक किस्तों में चुकाना है। प्रत्येक किस्त का अनुमानित मूल्य ज्ञात कीजिए।
₹11,922
₹12,522
₹11,524
₹11,022
उत्तर: C
हल: प्रत्येक वार्षिक किस्त x मानें। दोनों किस्तों का वर्तमान मूल्य लेने पर \(\frac{x}{1.1}+\frac{x}{1.1^2}=20000\)। इसलिए \(x(0.90909+0.82645)=20000\), जिससे \(x\approx11523.81\) मिलता है। अतः प्रत्येक किस्त लगभग ₹11,524 है। ट्रिक: चक्रवृद्धि ब्याज के गुणक से प्रत्येक भविष्य की किस्त का वर्तमान मूल्य निकालें।
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