A sum of money becomes Rs 17820 after 4 years and Rs 23760 after 6 years at compound interest, compounded annually. What is half of the sum, to the nearest rupee?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 5012
Under compound interest the amount is multiplied by the same growth factor every year. The ratio of the amounts 2 years apart gives the factor for 2 years, and going back 4 years from the 4-year amount gives the sum.
Growth factor for 2 years \(\displaystyle =\frac{23760}{17820}=\frac{4}{3}\)
Growth factor for 4 years \(\displaystyle =\left(\frac{4}{3}\right)^{2}=\frac{16}{9}\)
Sum \(\displaystyle =17820\div\frac{16}{9}=\frac{17820\times9}{16}=\) Rs 10023.75
Half of the sum \(\displaystyle =\frac{10023.75}{2}=5011.875\), which is Rs 5012 to the nearest rupee
Half of the sum is Rs 5012.