Question
Download Solution PDFRashid borrowed a sum of Rs. 30,240 at 10% p.a., interest compounded annually. If the amount is to be paid back in two equal annual installments, then the interest paid by him is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Principal = Rs 30,240
Rate = 10% p.a. interest compounded annually
Number of installments = 2
Formula Used:
For CI, in the case of equal installments
Principal = \(\frac{Installment}{(1+\frac{r}{100})}\) + \(\frac{Installment}{(1+\frac{r}{100})^2}\) + \(\frac{Installment}{(1+\frac{r}{100})^3}\) + ---- + \(\frac{Installment}{(1+\frac{r}{100})^n}\)
Calculation:
Let the installment be Y
⇒ Principal = \(\frac{Y}{(1+\frac{r}{100})}\) + \(\frac{Y}{(1+\frac{r}{100})^2}\)
⇒ 30,240 = \(\frac{Y}{(1+\frac{10}{100})}\) + \(\frac{Y}{(1+\frac{10}{100})^2}\)
⇒ 30,240 = \(\frac{Y}{(\frac{11}{10})}\) + \(\frac{Y}{(\frac{11}{10})^2}\)
⇒ 30,240 = Y × \(\frac{10}{11}\) + Y × \(\frac{100}{121}\)
⇒ 30,240 = Y × \(\frac{210}{121}\)
⇒ Y = 17,424
Total amount repaid by Rashid = 17,424 × 2 = Rs 34,848
Interest paid = 34,848 - 30,240 = Rs 4,608
∴ The interest paid by Rashid is Rs 4,608.
Last updated on Jul 4, 2025
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