A man invests Rs. 8000 at 80% per annum simple interest for 1 year and Rs. 12000 at 10% per annum compound interest for 2 years.
Find the total interest he received (in Rs).

The correct option is 8920.

To find the total interest received, we calculate the Simple Interest (SI) and Compound Interest (CI) separately and then add them together.

Step 1: Calculate the Simple Interest (SI)
Given:
Principal (P₁) = Rs. 8000
Rate of Interest (R₁) = 80% per annum
Time (T₁) = 1 year

${\mathrm{SI}}_{}=\frac{P_1\times R_1\times T_1}{100}$

${\mathrm{SI}}_{}=\frac{8000\times 80\times 1}{100}=6400$

Simple Interest received = Rs. 6400

Step 2: Calculate the Compound Interest (CI)
Given:
Principal (P₂) = Rs. 12000
Rate of Interest (R₂) = 10% per annum
Time (T₂) = 2 years

First, calculate the total Amount:

$\mathrm{Amount}=P_2{(1+\frac{R_2}{100})}^{T_2}$

$\mathrm{Amount}=12000{(1+\frac{10}{100})}^2$

$\mathrm{Amount}=12000\times {\left(\frac{11}{10}\right)}^2=12000\times \frac{121}{100}=14520$

Now, calculate Compound Interest (CI):

$\mathrm{CI}=\mathrm{Amount}-P_2=14520-12000=2520$

Compound Interest received = Rs. 2520

Step 3: Calculate the Total Interest

$\mathrm{Total\; Interest}=\mathrm{SI}+\mathrm{CI}=6400+2520=8920$

Thus, the total interest he received is Rs. 8920.