Question

A sum of Rs. 50000 amounts to Rs. 60500 after 2 years at a certain rate percent p.a when the interest is compounded annually. The same sum will amount to what after \(3\dfrac{1}{2}\) years at the same rate of interest? (nearest to a Rs.)
1. Rs. 69888
2. Rs. 69887
3. Rs. 69878
4. Rs. 69788

Answer 1

Correct Answer - Option 3 : Rs. 69878

Given:

P = 50000, A = 60500, T₁ = 2, R = ?

Formula used:

\(\Rightarrow Amount = P \times {\left( {1 + \frac{R}{{100}}} \right)^T}\)

Calculation:

\(60500 = 50000 \times {\left( {1 + \frac{{R}}{{100}}} \right)^2} \)

⇒ \({\left( {1 + \frac{{R}}{{100}}} \right)^2} = \frac{121}{100}\)

⇒ \({\left( {1 + \frac{{R}}{{100}}} \right)^2} = {\left( {\frac{{121}}{{100}}} \right)^2}\)

⇒ \({\left( {1 + \frac{{R}}{{100}}} \right)} = {\left( {\frac{{121}}{{100}}} \right)}\)

⇒ \(R = 21\%\)

Now; 

P = 50000, R = 21%, T₂ = \(3\dfrac{1}{2}\)

\(A= 50000 \times {\left( {1 + \frac{{21}}{{100}}} \right)^\frac{7}{2}} \)

⇒ \(A= 50000 \times {\left( {\frac{{121}}{{100}}} \right)^\frac{7}{2}} \)

⇒ \(A= 50000 \times {\left( {\frac{{11}}{{10}}} \right)^7} \)

⇒ A = 97435.85

Hence, "97435.85" is the correct answer.