Question
Download Solution PDFA sum of Rs. 10 is lent by a child to his friend to be returned in 11 monthly instalments of Rs. 1 each, the interest being simple. The rate of interest is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A sum of Rs. 10 is lent by a child to his friend to be returned in 11 monthly instalments of Rs. 1 each, the interest being simple.
Concept used:
Simple Interest, SI = (P × R × T)/100
Amount = P + SI
where
P = Principal amount
R = Rate of interest per year
T = Time in years
Calculation:
Let the rate of interest be R% p.a.
Total interest paid = 11 - 10 = Rs. 1
Since the installments are being paid monthly, the first, second, ...., and second-last EMI will incur interest for the next 10, 9, ...., and 1 month respectively. Since the last EMI completes the repayment, it will not incur any interest.
According to the concept,
(1 × R/100 × 10/12) + (1 × R/100 × 9/12) + (1 × R/100 × 8/12) + .... + (1 × R/100 × 1/12) = 1
⇒ \(\frac {R}{1200}\) (10 + 9 + ... + 1) = 1
⇒ \(\frac {R}{1200} \times \frac {11 \times 10}{2}\) = 1
⇒ R = 1200/55
⇒ R = \(21{ 9 \over 11}\)%
∴ The rate of interest is \(21{ 9 \over 11}\)%.
Last updated on Jun 13, 2025
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