Question

Mr. Mehra is planning for higher education expenses of his two sons aged 15 and 12. He plans to divide Rs 15 lakhs in two equal parts and invest in two different plans such that his sons may have access to Rs 21 lakhs each when they reach the age of 21. He is looking for plans that will give him a simple interest per annum. The rates of interest of the plans for his younger son and his elder son should be

• A. 5% and 7.5% respectively
• B. 8% and 12% respectively
• C. 10% and 15% respectively
• D. 15% and 22.5% respectively
• E. 20% and 30% respectively

Hint:

For simple interest, \(A=P(1+rt)⇒ r=\dfracA/P-1t\).
When targets and principals are proportional, compute \(A/P\) first to simplify calculations.

Answer 1

Answer: (E)

Step 1: Principal for each son is \(P=\) Rs \(7.5\) lakhs, target amount \(A=\) Rs \(21\) lakhs. For simple interest, \[ A=P(1+rt)\ ⇒\ r=\frac{A/P-1}{t}. \] Since \(A/P=21/7.5=2.8\), we have \(A/P-1=1.8\).
Step 2: Younger son (age \(12⇒ t=9\) years): \(r=\frac{1.8}{9}=0.2=20%\).
Elder son (age \(15⇒ t=6\) years): \(r=\frac{1.8}{6}=0.3=30%\).