Question
Rahul deposited an amount βQβ 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 βQβ 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 Γ r% Γ 1 = 300 β¦ (i)
Also, ((Q + 300) + 600) Γ r% Γ 1 = 5280 β ((Q + 300) + 600)
(Q + 900) Γ r% = 5280 β Q
(Q + 900) Γ (300/Q) = 5280 β Q
300Q + 270000 = 5280Q β QΒ²
QΒ² β 4980Q + 270000 = 0
QΒ² β 4800Q β 180Q + 270000 = 0
Q (Q β 4800) β 180 (Q β 4800) = 0
(Q β 4800)(Q β 180) = 0
Q = 4800 and Q = 180
Therefore, required interest = 4800 Γ [(1 + 10/100)Β² β 1] = 4800 Γ (1.21 β 1) = Rs. 1008
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