Joseph deposited a total of ₹52,500 in a bank in the names of his two daughters aged 15 years and 16 years in such a way that they would get equal amounts when they become 18 years old. If the bank gives 10% compound interest compounded annually, then what is the amount (in ₹) that Joseph had deposited in the name of his younger daughter?
Answer & explanation
Correct answer: option 3
Amount given to younger daughter = A
Amount given to elder daughter = ( 52500 - A )
Amount younger daughter get after 3 years = Amount elder daughter get after 2 years
A × ( 1 + \(\frac{rate }{100}\) )³ = (52500-A) × ( 1 + \(\frac{rate }{100}\) )²
A × ( 1 + \(\frac{10 }{100}\) )³ = (52500-A) × ( 1 + \(\frac{10 }{100}\) )²
A ×\(\frac{11 }{10}\)×\(\frac{11 }{10}\)×\(\frac{11 }{10}\) = ( 52500-A)×\(\frac{11 }{10}\)×\(\frac{11 }{10}\)
A ×\(\frac{11 }{10}\) = 52500 - A
\(\frac{11A }{10}\) + A = 52500
\(\frac{21A }{10}\) = 52500
A = Rs. 25000