Continuous annuity question

[bip30]

A 10-year continuous annuity has a payment rate at time t of:
Rt = 100 - .09t^2, 0<=t<=10.

If deltat = 3/(100+3t), t>= 0, find the present value of the annuity.

The answer should be 850.

Please help, I don't really know how to go about this problem.
Thanks!

[no driver]

The PV of an annuity with a continuously variable rate of payment and a continuously variable rate of interest is


So, we have


Solving the inner integral:






So now we have:

[MyKenk]

Curse you and you're Tex'ing abilities No Driver!

One of these days... post Nov. 8th, I'm gonna take a look at that stuff...

alternately, you know delta(t) = 3/(100+t) = (3/100)/(1+t/100) = 3 * (.01/(1+.01t)). From that last form, you know that the accumulation function is a(t) = (1+.01t)^3, and that the discount function is (1+.01t)^1/3.

to discount to time zero, you need to divide all payments by the discount function at the time the payment is made, and sum them up (with an integral, over 0 to 10.)

Or, all i've managed to do is make a more complicated integral... well, i have it typed out, so pc=pc+1.

No Driver did it very well, ignore me, been a long day.

[no driver]

Originally Posted by mykenk

Curse you and you're Tex'ing abilities No Driver!

Once you get it typed up it's a lot of cut and paste, change a few things, cut and paste again. I started by copying the formula out of the list I posted in the sticky and it went pretty quickly after that. It took me two tries to work the problem because I didn't get the inner integral right the first time (didn't take the reciprocal of the fraction ) so I ended up spending more time on the problem than on answering the post.

When you decide to look into it more, http://www.forkosh.com/mimetex.html is your friend.

[bip30]

thank you, got it now.