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
