Question

In how many years will the sum of 3000at 20% per annum compounded semi annually become 3993

Answer 1

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

☛ When rate is compounded semi - annually :- We know that semi - annually or Half yearly Means Half of a year, when we Multiply it with 2 we will get a year .

So we can say that in this case :-

• Rate is Divided by 2.
• Time is Multiply by 2 . ( To make it a complete year).

Sᴏʟᴜᴛɪᴏɴ :-

➼ Principal = P = Rs.3000

➼ Rate = 20% per annum compounded semi annually = (20/2) = R = 10% annually .

➼ Amount = A = Rs.3993

➼ Time = Let T . ( after Mulitiply by 2.)

➼ A= P[ 1 + (R/100)]^T

➼ 3993 = 3000[ 1 + (10/100)]^T

➼ (3993/3000) = [ 1 + (10/100)]^T

➼ (1331/1000) = [ 1 + (10/100)]^T

➼ (11/10)³ = [ 1 + (10/100)]^T

➼ [ 1 + (1/10)]³ = [ 1 + (10/100)]^T

Comparing we get ,

➼ T = 3 Years.

Therefore,

➼ Actual Time = (3/2) = 1.5 Years. (Ans.)

Hence, Time period is 1.5 Years.

Answer 2

Given:

years will the sum of 3000at 20% per annum compounded semi annually become 3993

To find:

In how many years will the sum of 3000at 20% per annum compounded semi annually become 3993

STEP BY STEP EXPLANATION:

refer to the attachment

time taken is 3 half years or 11/2 years$.$