Given:

• Difference between compound interest (CI) and simple interest (SI) for 2 years = Rs. 90
• Rate of interest (R) = 12% per annum
• Time for final amount calculation = 3 years
• Interest is compounded annually

Step 1: Find the Principal (P)

The formula for the difference between compound and simple interest for 2 years is:

Difference=P×(R100)2\text{Difference}=P\times \left(\frac{R}{100}\right)^2Difference=P×(100R​)2

Substitute the known values:

90=P×(12100)2=P×14410,000=P×0.014490=P\times \left(\frac{12}{100}\right)^2=P\times \frac{144}{10,000}=P\times 0.014490=P×(10012​)2=P×10,000144​=P×0.0144

P=900.0144=6250P=\frac{90}{0.0144}=6250P=0.014490​=6250

So, the principal amount is Rs. 6250.

Step 2: Calculate the Amount at the end of 3 years with Compound Interest

The compound interest formula for amount is:

A=P×(1+R100)TA=P\times \left(1+\frac{R}{100}\right)^TA=P×(1+100R​)T

A=6250×(1+12100)3=6250×(1.12)3A=6250\times \left(1+\frac{12}{100}\right)^3=6250\times (1.12)^3A=6250×(1+10012​)3=6250×(1.12)3

Calculate (1.12)3(1.12)^3(1.12)3:

1.123=1.4049281.12^3=1.4049281.123=1.404928

Thus,

A=6250×1.404928=8780.80A=6250\times 1.404928=8780.80A=6250×1.404928=8780.80

Final Answer:

The value of the amount at the end of 3 years, compounded annually, is Rs. 8780.80