A bank loaned out $120,000, part of it at the flat rate of 12% per year and the rest at the flat rate of 6% per year. If, after one year, the total interest received on both loans was $13,200, how much was loaned at 12%

? (Simple interest is paid once, at the end of the year.) answer this in whole number

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.

Learn how to calculate interest rates on loans where $120,000 is split between 12% and 6% rates. After one year, the total interest received is $13,200. Detailed step-by-step solution provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation