Test Index

MAT Exam 2025 Paper

Question : 74 of 150

Marks: +1, -0

6,40,000

Solution:

Concept:

Simple interest equals compound interest for the same principal and period.

Given:

P = 6,40,000

R = 4.15\%

T = 3

years

9

months

= 3.75

years.

We need the compound interest rate

r

for 2 years such that

\mathrm{CI} = \mathrm{SI}

Explanation:

Step 1: Calculate simple interest.

\mathrm{SI} = \frac{P \times R \times T}{100}

= \frac{6,40,000 \times 4.15 \times 3.75}{100}

= ₹99,600

Step 2: Write compound interest for 2 years.

\mathrm{CI} = P\left(1+\frac{r}{100}\right)^{2} - P

= P\left[\left(1+\frac{r}{100}\right)^{2}-1\right]

Step 3: Set

\mathrm{CI} = \mathrm{SI}

6,40,000\left[\left(1+\frac{r}{100}\right)^{2}-1\right] = 99,600

\left(1+\frac{r}{100}\right)^{2}-1 = \frac{99,600}{6,40,000} = 0.1556

\left(1+\frac{r}{100}\right)^{2} = 1.1556

1+\frac{r}{100} = \sqrt{1.1556} = 1.075

\frac{r}{100} = 0.075

r = 7.5\%

Answer:

Rate of compound interest =

7.5\%

Correct option: C. 7.5%

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