Question

কোনো মূলধনের 2 বছরের সরল সুদ ও চক্রবৃদ্ধি সুদ যথাক্রমে 8400 টাকা এবং 8655 টাকা মূলধন ও সুদের হার কত​

Answer 1

Given:

The simple interest and compound interest of a certain sum of money for two years are ₹ 8400 and ₹ 8655

To find:

The sum of money and the rate of interest

Solution:

We have the formulas of calculating the S.I. and C.I. as follows:

$\boxed{\bold{S.I. = \frac{PRT}{100} }}$

$\boxed{\bold{C.I. = P [(1 + \frac{R}{100} )^n - 1] }}}$

If we Substitute the no. of years = 2 years and then divide the formula of C.I. by S.I., then we will get the following formula for calculating the rate of interest for 2 years:

$\boxed{\bold{R\% = 2 \times \frac{C.I. - S.I. }{S.I.} \times 100 }}$

Here we have,

C.I. = Rs. 8655

S.I. = Rs. 8400

On substituting the values in the formula, we get

$R\% = 2 \times \frac{8655 - 8400 }{8400} \times 100 }} = 2 \times \frac{255 }{8400} \times 100 = \bold{6\%}$

Now, on substituting the value of R in the formula of S.I., we get

$8400 = \frac{P \times 6 \times 2}{100}$

$\implies P = \frac{840000}{12}$

$\implies \bold{P = 70,000}$

Thus,

The sum of money is Rs. 70,000.

The rate of interest is 6% p.a..

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