Final answer:
The annual effective interest rate can be calculated using two pieces of financial information given. By setting up an equation system with the present value of payments over 2n years and an n-year deferred annuity-immediate, we can solve for the interest rate, although the calculations might require numerical methods.
Step-by-step explanation:
To calculate the annual effective interest rate i, we need to consider two separate pieces of information given in the question:
- The present value of payments for 2n years, including an additional payment during the first n years.
- The present value of an n-year deferred annuity-immediate paying 2 per year for n years.
For the first part, the present value (PV) of receiving 2 at the end of each year for 2n years, plus an additional 1 for the first n years, is:
PV1 = 2 * (1 - (1+i)^(-2n)) / i + 1 * (1 - (1+i)^(-n)) / i = 36
For the second part:
PV2 = 2 * (1 - (1+i)^(-n)) / i * (1/(1+i)^n) = 6
From here, an equation system is obtained that can be solved for i and n. The actual calculation can be complex and may require iterative methods or financial calculators to solve for the interest rate i.
An example that follows a similar concept would be a simple two-year bond with an annual interest rate of 8%. The bond's present value calculation at various discount rates demonstrates how to apply the present value formula to determine the value of future cash flows.