Mr Shridharan invested money in two schemes A and B, offering compound interest @ 8 p.c.p.a and 9 p.c.p.a respectively. If the total amount of interest accrued through the two schemes together in two years was Rs. 4818.30 and the total amount invested was Rs. 27,000, what was the amount invested in scheme A?
Solution
Correct Answer: Option C
Let the amount invested in scheme A at a rate of interest 8% p.c.p.a be P
Investment in scheme B at a rate of interest 9% p.c.p.a = 27000 – P
In Compound Interest,
\(A = P{\left. {\left( {1 + \frac{r}{{100}}} \right.} \right)^n}\)
Where A is Amount after n years, P is Principal, r is Rate of Interest and n is the number of years.
Amount due to scheme \(A = P{\left. {\left( {1 + \frac{8}{{100}}} \right.} \right)^2} = 1.08^2\ P = 1.1664\ P\) -------------------- (A)
Amount due to scheme \(A = \left( {27000 - P} \right){\left. {\left( {1 + \frac{9}{{100}}} \right.} \right)^2} = 32078.70-1.1881\ P\) ----- (B)
⇒ Total Interest = Total Amount – Total Principal
⇒ 4818.30 = (1.1664P + 32078.70 – 1.881P) – 27000
⇒ 0.0217P = 260.40
⇒ P = 12000
∴The amount invested in scheme A is Rs. 12000.
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