Let's denote the amount loaned at 12% as $x$, and the amount loaned at 6% as $120,000 - x$.

The interest received from the amount loaned at 12% is: $\text{Interest at 12\%} = 0.12 \times x$

The interest received from the amount loaned at 6% is: $\text{Interest at 6\%} = 0.06 \times (120,000 - x)$

The total interest received after one year is the sum of these two amounts: $0.12x + 0.06(120,000 - x) = 13,200$

Now, let's solve this equation for $x$.

1. Distribute the 0.06: $0.12x + 0.06 \times 120,000 - 0.06x = 13,200$ $0.12x + 7,200 - 0.06x = 13,200$

2. Combine like terms: $0.06x + 7,200 = 13,200$

3. Subtract 7,200 from both sides: $0.06x = 6,000$

4. Divide both sides by 0.06 to solve for $x$: $x = \frac{6,000}{0.06} = 100,000$

So, the amount loaned at 12% is $100,000.

Would you like a detailed breakdown or have any further questions?

Related Questions:

1. How much was loaned at 6%?
2. What would the interest be if the entire $120,000 was loaned at 12%?
3. What would the interest be if the entire $120,000 was loaned at 6%?
4. What is the total interest received after 2 years?
5. How would the loan amount change if the interest rates were swapped?
6. What if the total interest received was $15,000 instead of $13,200?
7. What is the percentage of the total loan that was lent at 12%?
8. How much would the interest be if the loan at 12% was $80,000?

Tip:

Always double-check your final steps to ensure accuracy in calculations, especially in financial problems.