A sum of money was divided into 2 parts in the ratio 2 : 5. The first part was invested for 2 years at the annual interest rate of 20% compounded annually. At what rate of simple interest per annum must the second part be invested for 2 years, so that the interest earned in both cases is the same?

Answer (Detailed Solution Below)View answer ▾

Answer: Option C — 8.8%

Detailed Solution

Let the parts be $2 k$ and $5 k$ .

Compound interest on $2 k$ for 2 years at 20 percent: $2 k (1.2^{2} - 1) = 2 k (0.44) = 0.88 k$ .

Simple interest on $5 k$ for 2 years at R percent: $\frac{5 k \times R \times 2}{100} = 0.1 R k$ . Equating, $0.1 R = 0.88$ , so R = 8.8 percent.

✓ Check

With

k = 100

: CI on 200 is

200 \times 0.44 = 88

, and SI on 500 at 8.8 percent for 2 years is

500 \times 0.088 \times 2 = 88

⚠ Common trap

Using simple interest for the first part too gives

0.8 k

and R = 8 percent, not an option; the 20 percent is compounded.

Quick tip

$2 (1. 2^{2} - 1) = \frac{5 \cdot 2 R}{100} \Rightarrow R = 8.8$

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Simple & Compound Interest — Preparation

This question tests your understanding of Simple & Compound Interest, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.

Simple interest is calculated only on the original principal, while compound interest is calculated on the principal plus interest already earned. Questions test the formulas SI = PRT/100 and A = P(1 + R/100)^n, the difference between CI and SI over two or three years, interest compounded half-yearly or quarterly, instalments, and the time needed for money to double or triple. Useful shortcuts include the two-year CI minus SI difference, which equals P(R/100)^2, and the effective-rate method, which treats two years of compounding at R% as a single percentage change. Connecting interest to successive percentage change makes most compound interest questions much faster than expanding the formula. Practise the simple and compound interest questions below. Each comes with a full solution and a shortcut where one applies.

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A sum of money was divided into 2 parts in the ratio 2 : 5. The first part was invested for 2 years at the annual interest rate of 20% compounded annually. At what rate of simple interest per annum must the second part be invested for 2 years, so that the interest earned in both cases is the same?

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Simple & Compound Interest — Preparation