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Hi I was wondering how do I Solve this question. I have to solve for the root. I can solve for it when there's one summation but it's nested. I'm not that good at solving summations, if I can get some guidance please. Question is related to https://money.stackexchange.com/posts/36903/edit What does {p,0} mean? I haven't seen that notation.

Principal: $100,000  
Interest Rate: 8.5%  
Periods: 120  
Payment Frequency: Monthly  
Disbursal Date: January 1st 2014    
Compounding Semi-Anually

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  • It is the initial guess of the solution of the variable $p$. Try with {p,1000}. In fact this kind of problem is so well conditionned that you could almost start from anywhere. – Claude Leibovici Sep 12 '14 at 17:08

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I gave you in a comment the meaning of {p,0} as you required.

Now, let us look at the real problem : there is only one place where $p$ appears and then the equation will just be linear in $p$; so you can start whereven you want the iterative procedure $FindRoot$; another solution is to compute the lhs for two different values of $p$ and compute the equation of the straight line and solve for the value you want.

You could also notice that the sums can be computed analytically (keeping $e$,$r$,$y$ as letters up to the end. Remeber that $$\sum_{k=m}^{k=n}\frac{1}{(1+r)^k}=\frac{(r+1)^{1-m}-(r+1)^{-n}}{r}$$

Using your values, the equation for the lhs is simply $39.7392 (1.0425 p+500)$ and you want that to be equal to a value $a$.So, $p=0.0241382 a-479.616$ and if $a=100000$, $p=1934.2$.

Claude Leibovici
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