To calculate the interest earned on an investment with compound interest, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed.
In this case:
- \( P = 13000 \)
- \( r = 0.12 \) (12% as a decimal)
- \( n = 12 \) (compounded monthly)
- \( t = 14 \)
Plugging in these values:
\[ A = 13000 \left(1 + \frac{0.12}{12}\right)^{12 \times 14} \]
First, calculate \( \frac{0.12}{12} \):
\[ \frac{0.12}{12} = 0.01 \]
Then update the equation:
\[ A = 13000 \left(1 + 0.01\right)^{168} \] \[ A = 13000 \left(1.01\right)^{168} \]
Next, calculate \( (1.01)^{168} \):
\[ (1.01)^{168} \approx 4.033571 \]
Now we can calculate \( A \):
\[ A = 13000 \times 4.033571 \approx 52436.42 \]
Now, we need to find the interest earned:
\[ \text{Interest} = A - P \] \[ \text{Interest} = 52436.42 - 13000 = 39436.42 \]
So, the interest earned in 14 years is approximately:
\[ \boxed{39436.42} \]