Final answer:
Compound interest is the interest calculated on the principal and the accumulated interest over time. The future value is calculated using the formula: Future Value = Principal x (1 + interest rate)^time, and the present value considers the time value of money. Simple interest is the non-compounded interest calculated using the formula: Total future amount = Principal + (Principal x interest rate x time).
Step-by-step explanation:
Computing for compound amounts, compound interests, and present values involves the application of specific financial formulas. To calculate the future value which is the compound amount, you can use the following formula: Future Value = Principal x (1 + interest rate)^time. The compound interest is then found by subtracting the present value (original principal amount) from the future value.
For a practical example, consider a principal of $1,000 at an annual interest rate of 5% compounded annually for 3 years. The future value formula would look like this:
- Future Value = $1,000 x (1 + 0.05)^3
After calculating the future value, subtract the original principal to get the compound interest. To find the present value of an amount due in the future, you can use the present value formula which considers the discounting effect of the interest rate over time.
When you add up all present values for different time periods, you determine the total present value at a 15% interest rate. This reveals what future amounts are worth today. For comparison, the total future amount with simple interest would be calculated without compounding, as shown by the formula: Total future amount = Principal + (Principal x interest rate x time).