Question 1

# Given below are two statements : Statement I: A savings account at Bank A pays 6.2% interest, compounded annually. Bank B's savings account pays 6% compounded semi-annually. Bank B is paying less total interest each year. Statement II: A sum of money at a certain rate of compound interest doubles in 3 years. In 9 years, it will be P times original principal. Then P = 9. In the light of the above statements, choose the correct answer from the options given below.

Solution

Statement I:

Bank A:Â r = 6.2% and compounded anually

Compound interest at the end of an year =Â $$P\left(1+\frac{6.2}{100}\right)-P=\frac{6.2P}{100}$$

Bank B:Â r = 6% and compounded semi-anually

C.I =Â $$P\left(1+\frac{3}{100}\right)^2-P=\frac{P\left(6.09\right)}{100}$$

Interest is less in bank B.

Therefore, statement I is correct.

Statement II:

Let the sum of money be 'S'

It is given,

$$S\left(1+\frac{r}{100}\right)^3=2S$$

$$\left(1+\frac{r}{100}\right)^3=2$$

$$\left(1+\frac{r}{100}\right)^9=4$$

$$S\left(1+\frac{r}{100}\right)^9=4S$$

Therefore, P = 4

Statement II is incorrect.

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