I’m having trouble transposing the formula for Present Value of an Ordinary Annuity in order to find the interest rate. The formula is: Where P=Present Value of an Ordinary Annuity PMT=Payment i=Interest Rate n=Number of Terms Not sure if it helps, but I managed to simplify the formula to this: Thanks in advance.

The problem statement is: What annual instalment will discharge a debt of 1092 due in 3 years at 12% simple interest? Now, what I know is Simple interest =( principal* Rate per annum*Time in years)/(100) Here, R= 12℅ ,T=3 years but I don’t understand how to move forward.I am not getting the meaning of the […]

Given odds $o_i$ for $i=1,2,\ldots,n$ and the possibility to bet the amount $b_i\in \mathbb{R}$ on each event such that if event $i$ occurs you receive $b_io_i$ and if it doesn’t you recieve $-b_i$. I am trying to find out the condition for arbitrage. My immediate thoughts are that $1/o_i$ represents probability, and since these events […]

What’s the math formula that is used to calculate the monthly payment in this mortgage calculator? I would like to know this math formula so that I can plug in the following values Mortgage Amount: $100,000 Rate Type: Fixed Interest Rate: 6% Interest Term: 5 Years Payment Frequency: Monthly Amortization Rate: 5% and calculate the […]

What is an alternative book to oksendal’s stochastic differential equation: An introduction? But also An alternative that is over 300 pages and at the same level? Some professor refer that book as a bible for finance.

The compound interest formula is: $$A_t=A_0(1+r)^t$$ There is a simple derivation for this which works by starting with $A_1$ and then considering $A_2$ and then extrapolating. The above formula can be manipulated to solve any related problem we have. Rates are almost always stated as APR’s, which once stated are a legal obligation so daily […]

I’m a quantitative researcher at a financial company. I have a PhD in math, but I’m an algebraist, so I only took the two required analysis courses in grad school (measure theory for the first, and I don’t even remember the content of the second course. It involved Fourier series). I taught a probability course […]

I’m doing actuarial problems of Exam MFE and it covers some of the stochastic calculus (like Ito’s Lemma). One of the frequently used results are the so-called “multiplication rules”: $(dt)^2=0$ $dZ(t)^2=dt$ $dZ(t) \, dt=0$ I tried to do some research online. There are tons of papers providing introduction to stochastic calculus, but strangely all of […]

I’m a math student, starting a PhD in the near future. My field of research will be mostly in the field of applied mathematics / numerics. Topics will deal with Kinetic Theory, Moment Equations, Fractional Diffusion, Spetral Methods. I think I have a solid background in numerical computing, especially for PDEs. Now for my Masterthesis […]

I’m trying to show that the price of a European call option (payoff function is $(S_1-K)^+$) in a no-arbitrage market is a decreasing and convex function of K. That it shall be decreasing makes sense; as $K$ increases, $S_1-K$ decreases and we make less profit. But why shall it be convex?

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