A perpetuity-immediate pays 100 per year. Immediately after the fifth payment, the perpetuity is exchanged for a 25-year annuity-immediate that will pay X at the end of the first year. Each subsequent annual payment will be 5% greater than the preceding payment. The annual effective rate of interest is 8%. Calculate X.

X = 74.18

Step-by-step explanation:

Given that:

A perpetuity-immediate pays 100 per year and the annual effective rate of interest is 8%.

The PV of Perpetuity = = 1250

As this will be equivalent to the PV of the geometrically increase in annuity-immediate. Thus, the npv at time point S will be:

where

i = annual payment = 5% = 0.05

v = 1/1+ annual effective rate

= 1/1+8%

= 1/1+0.08

= 1/1.08

Our equation can be re-written as:

To determine the value of X, we equate the above value with 1250.

So, 16.35X = 1250

X =

X = 74.18

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