Find the principal if compound interest is charged on the principal at the rate of 16 2/3 \% per annum for 2 yr and the sum becomes ₹ 196.

Correct Answer is : None of these

Correct Answer is : None of these

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MAT Exam 2020 Paper

Question : 83 of 200

Marks: +1, -0

16 \frac{2}{3} \%

per annum for 2 yr and the sum becomes ₹ 196.

Solution:

Concept:

Compound interest amount formula is

A = P\left(1+\frac{r}{100}\right)^t

, where

A

is the amount,

P

is the principal,

r

is the rate per annum, and

t

is the time in years.

Explanation:

Given:

A = ₹ 196

r = 16\frac{2}{3}\% = \frac{50}{3}\%

, and

t = 2

years.

Convert the rate:

\frac{r}{100} = \frac{\frac{50}{3}}{100} = \frac{1}{6}

Substitute into the formula:

196 = P\left(1+\frac{1}{6}\right)^2

196 = P\left(\frac{7}{6}\right)^2

196 = P \times \frac{49}{36}

P = \frac{196 \times 36}{49}

P = 4 \times 36 = 144

Thus, the principal is ₹

144

Answer:

Principal

= ₹ 144

, so the correct option is D, None of these.

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