If the amount on the principal of Rs.6000 is written as $6000 1 + 5100 3$ and compound interest payable for 6 months, then the rate of interest p.a. is % and time is years.

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Detailed Solution

If the amount on the principal of Rs.6000 is written as

6000 1 + 5100 3

and compound interest payable for 6 months, then the rate of interest p.a. is 10 % and the time is 1.5 years.
It is given that the amount on the principal of Rs.6000 is

6000 1 + 5100 3 .

We know that,
If the interest is compounded for 6 months, then

C . I . = P 1 + R 200 2 t − P

And, the total amount s given by,
Amount = Principal Amount + C.I.
Therefore we have,

Amount = 6000 1 + 5100 3 ... (1)

Since the interest is compounded for 6 months, then

C . I . = P 1 + R 200 2 t − P

It is given that the principal amount = Rs.6000.

⇒ Amount = 6000 + 6000 1 + R 200 2 t − 6000

⇒ Amount = 6000 1 + R 200 2 t .... (2)

From equations (1) and (2), we get,

6000 1 + R 200 2 t = 6000 1 + 5100 × 22 3

⇒ 6000 1 + R 200 2 t = 6000 1 + 10200 3

By comparing both the sides, we will get

2 t = 3 and R = 10 .

∵ 2 t = 3 ⇒ t = 32 = 1.5

Therefore the rate of interest per annum is 10% and the time is 1.5 years.

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