Final answer:
The question requires calculating the duration of the perpetuity-immediate with varying initial payments and constant payments thereafter using an effective interest rate of 6%. the duration is determined by finding the weighted average time of the cash flows considering the time value of money. We use the present value of a perpetuity formula, adjusting for the initial non-level payments, and then apply the duration formula.
Step-by-step explanation:
The student asked for the calculation of the duration of a perpetuity-immediate with specific payment amounts for the first two years and level payments thereafter, given an annual effective interest rate of 6%. In order to calculate this, we need to find the present value of each of the perpetuity's cash flows, and then use this to determine the duration, or the weighted average time until the cash flows are received. to calculate the present value of the perpetuity's cash flows, we would use the formula for the present value of a perpetuity: PV = PMT / i, where PMT is the recurring payment and i is the interest rate per period. However, as the payments in the first two years differ, they need to be treated separately. The level payments starting from year three can be considered as a standard perpetuity.
The duration of a perpetuity is computed using a weighting approach, where each cash flow is multiplied by the time at which it occurs, and the sum is then divided by the total present value of the perpetuity. In abstract terms, duration is D = Σ(CFt /(1+i)t * t) / Σ(CFt /(1+i)t), where CFt represents the cash flow at time t, and i is the interest rate. For the first two payments, their individual present value, multiplied by the time they are received, will be incorporated into this formula.