# Financial Maths for ct1 (1 Viewer)

Hi,

#### Drongoski

##### Well-Known Member
What's that angled bracket on top of n? In my copy of "Higher Algebra" by Hall & Knight,(1955 Ed; 1st Edition 1887) there is something similar but the angled bracket appears on the lower left - this was the old notation for n!

#### BenHowe

##### Active Member
oh sorry I should've explained it, the LHS= the present value of a level increasing annuity payable continuously for n years at a rate of i percent p/a

#### InteGrand

##### Well-Known Member
$\bg_white \noindent Well here's some hints to at least evaluate that sum in your question. Once you evaluate the integral, you should see that you effectively need to compute a sum of the form$

$\bg_white S = \sum_{k=1}^{n}k v^{k-1}.$

$\bg_white \noindent There are a few ways to evaluate such a sum. Here's a hint for one method. I'll assume v \neq 1 (if v = 1, the series is just an arithmetic series).$

\bg_white \noindent Multiply both sides by v, so vS = \sum_{k =1}^{n} kv^{k}. Now see what you get if you consider S -vS (hint: align like powers of v). You should end up with something familiar that will let you solve for S. Hope this helps!

#### BenHowe

##### Active Member
I think I must be doing something wrong. For the summation I just want

$\bg_white \sum_{t=1}^{n}te^{-\delta t} \\ \text{However I get} \sum_{t=1}^{n} -\frac{t}{\delta}e^{-\delta t}[1-e^{\delta}]$

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#### Drongoski

##### Well-Known Member
oh sorry I should've explained it, the LHS= the present value of a level increasing annuity payable continuously for n years at a rate of i percent p/a
Oh yea. I should have remembered that notation.

#### BenHowe

##### Active Member
Oh yeah sorry I skipped stuff as well $\bg_white v=e^{-\delta}$, where v is (1+i)^-1, so discounting whatever for 1 period but delta is the force or the rate of interest payable continously. so v=(1+i)^-1=e^-delta

#### BenHowe

##### Active Member
Thanks for the help guys I realised my errors and can do it/understand it now. Thanks heaps! I'd upload the solution but I don't know how to put the actuarial angle in the bos LaTeX editor only on the LaTeX editor on my computer. That and you guys would find it very boring

#### BenHowe

##### Active Member
Hey,

I think the answer is yes but I can't clearly explain why. Help please

#### BenHowe

##### Active Member
Dw all good standard integral properties

#### Zoinked

##### Beast
this all looks cancerous, do we ever have to do stuff like this in applied finance or is this just actuarial work?

#### BenHowe

##### Active Member
No this is financial maths for actuaries. In saying that, you will encounter some of it like interest rates compounded continuously or momently etc. I just think the treatment of the material is a little different. I'll let you know though