A man takes a loan of 1000 and repays it by paying 530 at the end of the first year, and 594 at the end of the second year. Find the rate of interest per annum.

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

Step 1: Try \( r=8\% \) and track the loan year by year instead of discounting. Interest for year 1 on ₹1000 at 8% is ₹80, so the amount owed grows to \( 1000+80=1080 \).
Step 2: Pay ₹530. Remaining balance \( =1080-530=550 \).
Step 3: Interest for year 2 on ₹550 at 8% is ₹44, so the amount owed grows to \( 550+44=594 \).
Step 4: The second payment is exactly ₹594, which clears the balance to zero exactly, no leftover, no shortfall.

Since the numbers close perfectly at 8% with no approximation needed, this confirms:
\[ \boxed{r = 8\%} \]

A man takes a loan of 1000 and repays it by paying 530 at the end of the first year, and 594 at the end of the second year. Find the rate of interest per annum.

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The Correct Option is A

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