What is the Present Value of a Perpetuity with Increasing Payments?

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Consider a perpetuity, which makes payments twice a year. The first year payments are
5 at time 0.5 (years) and 5 at time 1, next year they are 10 at time 1.5 and 10 at time 2, in
the third year the payments are 15.
 
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sstark said:
Consider a perpetuity, which makes payments twice a year. The first year payments are
5 at time 0.5 (years) and 5 at time 1, next year they are 10 at time 1.5 and 10 at time 2, in
the third year the payments are 15.

Is there a question here somewhere?

RGV
 
Consider a perpetuity, which makes payments twice a year. The first year payments are
5 at time 0.5 (years) and 5 at time 1, next year they are 10 at time 1.5 and 10 at time 2, in
the third year the payments are 15 at time 2.5 and 15 at time 3, and so on. The annual
interest rate is 8% nominal convertible semiannually. Find the present value of this
perpetuity
 
sstark said:
Consider a perpetuity, which makes payments twice a year. The first year payments are
5 at time 0.5 (years) and 5 at time 1, next year they are 10 at time 1.5 and 10 at time 2, in
the third year the payments are 15 at time 2.5 and 15 at time 3, and so on. The annual
interest rate is 8% nominal convertible semiannually. Find the present value of this
perpetuity

OK. Now show us what you have done. Forum rules require you to show an attempt first before receiving any help.

RGV
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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