To find the uniform series over the interval [11, 20] that is equivalent to the uniform series of $10,000 cash flows over the interval [1, 10] based on a 10% annual compound interest rate, we can use the formula for the present value of an ordinary annuity.
Step-by-step explanation:
1. The formula for the present value of an ordinary annuity is:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
where PV is the present value, PMT is the periodic payment, r is the interest rate, and n is the number of periods.
2. In this case, the periodic payment (PMT) is $10,000, the interest rate (r) is 10% or 0.1, and the number of periods (n) is 10.
3. We want to find the equivalent uniform series over the interval [11, 20]. Since the intervals are shifted by 10 periods, we need to calculate the present value for 10 periods less.
4. To calculate the present value of the equivalent uniform series over the interval [11, 20], we substitute the values into the formula:
PV = $10,000 * [(1 - (1 + 0.1)^(-10)) / 0.1]
5. Simplifying the equation, we get:
PV = $10,000 * [(1 - (1.1)^(-10)) / 0.1]
6. Evaluating the expression, we find that the present value of the equivalent uniform series over the interval [11, 20] is approximately $46,578.23.
In conclusion, the uniform series over the interval [11, 20] that is equivalent to the uniform series of $10,000 cash flows over the interval [1, 10] based on a 10% annual compound interest rate is approximately $46,578.23.