Discussion
Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
Answer: A
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
Track the debt in two stages.
First two years:
\[ 4000 \times (1.05)^{2} = 4000 \times 1.1025 = \text{Rs. } 4410 \]
He repays Rs. 2210, leaving Rs. 2200.
Next two years:
\[ 2200 \times (1.05)^{2} = 2200 \times 1.1025 = \text{Rs. } 2425.50 \]
\[ \text{total repaid} = 2210 + 2425.50 = \text{Rs. } 4635.50 \]
\[ \text{interest} = 4635.50 - 4000 = \text{Rs. } 635.50 \]
The part-payment reduces the balance that compounds thereafter, so it must be subtracted before the second stage begins.
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