Kate has a sum of Rs. 14000 that she divided into two equal parts. She invested the first part in compound interest at 15% per annum rate of interest for two years. After two years, she withdrew the whole amount and invested it and second part in simple interest at 12% per annum rate of interest. How much money she will have after 4 years?
Solution
Correct Answer: Option E
Two equal parts of Rs. 14000 will be Rs. 7000 and Rs. 7000.
Kate invested the first part in compound interest at 15% per annum rate of interest for two years.
We know, amount = Principal × \(\left[ {{{\left( {1{\rm{\;}} + {\rm{\;}}\frac{{\rm{R}}}{{100}}} \right)}^{\rm{T}}}} \right]\)
Amount that Kate has after two years = 7000 + 7000 × \(\left[ {{{\left( {1\; + \;\frac{{15}}{{100}}} \right)}^2}} \right]\)
= 7000 + (7000 × 1.3225) = 16257.5
After two years, she withdrew the whole amount and invested it and second part in simple interest at 12% per annum rate of interest.
Simple interest = (Principal × Rate × Time)/100
Amount = Principal + Simple Interest
Amount that Kate has after 4 years = 16257.5 + (16257.5 × 12 × 2)/100 = 16257.5 + 3901.8 = 20159.3
∴ Kate will have Rs. 20159.3 after 4 years.
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