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

Question

Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is

Answer 1

Approach: Don't solve a quadratic at all. CAT gives you four clean rate options, so just test them by tracking the outstanding balance year by year and check which one clears the loan exactly.

Step 1: The rule: each year the balance grows by the rate, then the instalment is subtracted. The correct rate leaves a zero balance after the second payment.

Step 2: Test $r = 8\%$. After year 1 the loan becomes $1000 \times 1.08 = 1080$. Pay Rs 530, leaving $1080 - 530 = 550$.

Step 3: That Rs 550 grows for the second year: $550 \times 1.08 = 594$. Pay the second instalment of Rs 594, leaving $594 - 594 = 0$.

Step 4: The balance vanishes exactly, so $8\%$ is correct. (Quick sanity check: at $7\%$, $1000 \times 1.07 - 530 = 540$, then $540 \times 1.07 = 577.8 \ne 594$, so it fails.)

Final answer: $8\%$.

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

Show Hint

The Correct Option is C

Solution and Explanation

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