Question
Rahul deposited an amount ‘Q’ in a plan A and earned
Rs. 300 as interest after one year. He then added Rs. 600 to the amount and re-invested the entire sum in the same plan A for another year. After the second year, he received Rs. 5280 as the total amount. Find the interest earned if the amount ‘Q’ was invested in a different scheme B offering 10% compound interest per annum for 2 years.Solution
ATQ,
Let, rate of interest be r% per annum.
Q × r% × 1 = 300 … (i)
Also, ((Q + 300) + 600) × r% × 1 = 5280 – ((Q + 300) + 600)
(Q + 900) × r% = 5280 – Q
(Q + 900) × (300/Q) = 5280 – Q
300Q + 270000 = 5280Q – Q²
Q² – 4980Q + 270000 = 0
Q² – 4800Q – 180Q + 270000 = 0
Q (Q – 4800) – 180 (Q – 4800) = 0
(Q – 4800)(Q – 180) = 0
Q = 4800 and Q = 180
Therefore, required interest = 4800 × [(1 + 10/100)² – 1] = 4800 × (1.21 – 1) = Rs. 1008
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