A loan of Rs 1000 is fully repaid by two installments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is

✅ Correct Option: 3

Let the rate of interest be $r\%$ per annum.

At the end of Year 1, the amount owed on the loan:

$= 1000 \times \left(1 + \dfrac{r}{100}\right)$

After paying the first installment of Rs 530, the remaining balance:

$= 1000\left(1 + \dfrac{r}{100}\right) - 530$

This remaining balance grows with interest for one more year and must exactly equal the second installment of Rs 594:

$\left[1000\left(1 + \dfrac{r}{100}\right) - 530\right] \times \left(1 + \dfrac{r}{100}\right) = 594$

Trying $r = 8$ :

Amount after Year 1 $= 1000 \times 1.08 = 1080$

Balance after first installment $= 1080 - 530 = 550$

Amount after Year 2 $= 550 \times 1.08 = 594$

This equals the second installment exactly.

The rate of interest is $8\%$ .

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A loan of Rs 1000 is fully repaid by two installments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is

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