To determine the total interest earned or repaid on an investment or loan of 1000 over five years with an interest rate of 10% per annum, compounded monthly, we'll 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 money invested or borrowed), which is 1000.
• $r$ is the annual interest rate (decimal), which is 0.10 for 10%.
• $n$ is the number of times that interest is compounded per year, which is 12 for monthly compounding.
• $t$ is the time the money is invested or borrowed for, in years, which is 5 years.

Let's calculate the total amount and then the interest earned/repaid.

Step 1: Calculate the accumulated amount $A$.

$A = 1000 \left(1 + \frac{0.10}{12}\right)^{12 \times 5}$

Step 2: Calculate the interest earned/repaid.

$\text{Interest} = A - P$

I'll compute this now.The total amount accumulated after five years is approximately 1645.31. Therefore, the total interest earned or repaid is approximately 645.31.

Would you like further details or have any questions?

Here are five related questions for further exploration:

1. How would the interest change if the rate was 8% instead of 10%?
2. What is the effect of compounding quarterly instead of monthly?
3. How would the interest differ if the investment period was only 3 years?
4. What would be the future value if 2000 were invested under the same conditions?
5. How does simple interest compare to compound interest in this scenario?

Tip: The frequency of compounding (monthly, quarterly, etc.) significantly impacts the total interest accumulated over time. The more frequent the compounding, the higher the final amount.