Final answer:
To calculate the amount owed after 9 years on a $2000 loan with a 7.5% interest rate compounded monthly, the compound interest formula is used. The principal amount and interest are plugged into the formula, which will yield the total amount owed including the compounded interest.
Step-by-step explanation:
To find the amount owed after 9 years on a loan of $2000 with a 7.5% interest rate compounded monthly, we can use the compound interest formula:
A = P ( 1 + \frac{r}{n} \right)^{nt}
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount ($2000).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
So, plugging in the values:
A = $2000 ( 1 + \frac{0.075}{12} \right)^{12(9}
By calculating this, we can find the total amount owed after the 9 years. Remember, the interest rate should be converted to a decimal by dividing by 100, and the final figure you'll arrive at will include the initial principal as well as the compounded interest.