Question
A certain sum of money is invested at simple interest at
a rate of R% per annum. I) When it is invested at this rate R% for 5 years, the interest earned is Rs 11,200. II) When the same sum is invested at a rate 2% higher (i.e. (R + 2)% p.a.) for 3 years, the interest earned is Rs 8,400. What is the value of R?Solution
ATQ, Let the principal (sum invested) be P and original rate be R%. From the first condition (rate = R%, time = 5 years): Simple Interest = P × R × 5 / 100 = 11,200 ⇒ (P × R) / 100 = 11,200 / 5 = 2,240 …(1) From the second condition (rate = R + 2, time = 3 years): Simple Interest = P × (R + 2) × 3 / 100 = 8,400 ⇒ (P × (R + 2)) / 100 = 8,400 / 3 = 2,800 …(2) Now subtract (1) from (2): (P(R + 2))/100 − (PR)/100 = 2,800 − 2,240 Left side = P×2/100 = 2P/100 So: 2P/100 = 560 ⇒ P/50 = 560 ⇒ P = 560 × 50 = 28,000 Now use (1) to find R: (PR)/100 = 2,240 (28,000 × R)/100 = 2,240 280R = 2,240 R = 2,240 / 280 = 8 So, the original rate of interest R = 8% per annum.
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