An equal sum is invested in two different schemes. One scheme gives simple interest and the other gives compound interest (annual compoundi… — Answer & Discussion

An equal sum is invested in two different schemes. One scheme gives simple interest and the other gives compound interest (annual compounding). The total interest obtained after 2 years from both the schemes together is Rs. 2090. If both the schemes have 18% per annum interest rate, then what is the first year interest (in Rs) of simple interest scheme?

A1000
B500
C545
D1045

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Discussion 1

CCommunity17 May 2019

Let P = 100 units

R = 18%/year = 18/100

Effective rate of C.I. for 2 years = 18% + 18% + (18 × 18)/100 = 39.4%

(S.I. + C.I.) of 2 years = 2090

⇒ (100 × 18 × 2 ) /100 + 100 × 39.4/100 = 2090

⇒ (36 + 39.4) units = 2090

⇒ 75.4 units = 2090

⇒ 1 unit = 2090/75.4 = 27.719

P = 100 units = 27.719 × 100 = 2771.9 ≈ 2772 (approx.)

∴ S.I. of 1 year = (2772 × 18 × 1)/100 = 498.96 ≈ 500 approx.