Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

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2
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2answers
2k views

Repayments of a loan with compound interest

Suppose I have a loan of M dollars. At the end of each year, I am charged interest at rate R and make a repayment of P. The loan is repaid after n years. How long (n) does it take to repay the loan ...
2
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2answers
450 views

Baseball betting and probablity

Here is a question that came up during class discussions on Friday: Your favorite baseball team is playing against your uncle's favorite team in the World Series. At the beginning of each game, you ...
1
vote
1answer
128 views

american put option

For a perpetual american put option $v(s)$, satisfies the following problem: $$\frac12\sigma^2S^2\frac{\mathrm d^2V}{\mathrm dS^2}+(r-D)S\frac{\mathrm dV}{\mathrm dS} - rV = 0\quad\text{for ...
0
votes
1answer
350 views

How to calculate APR using Newton Raphson

I'm have a computer program to calculate apr using Newton Rhapson. I imagine most mathletes can code so i dont imagine the coding being an issue. The solution is based on this initial formula ...
4
votes
2answers
229 views

What's the math formula that is used to calculate the monthly payment in this mortgage calculator?

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 ...
1
vote
1answer
412 views

today's price of a European put option with payoff $(K-S_1)^+$

I'm trying to calculate the today's price of a European put option, which strikes at price $K$, so that the payoff is $(K-S_1)^+$, in an arbitrage-free, one-period market. As of now, I can only think ...
1
vote
3answers
7k views

Most efficient method for converting flat rate interest to APR.

A while ago, a rather sneaky car salesman tried to sell me a car financing deal, advertising an 'incredibly low' annual interest rate of 1.5%. What he later revealed that this was the 'flat rate' ...
1
vote
1answer
3k views

How the formula for EMI is derived

I was looking for a formula to calculate EMI (Equated Monthly Installments). I have some fixed known parameters like, Principal Amount, Rate of Interest and No. Of Installments. By googling, I came ...
0
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2answers
215 views

Resolving a paradox concerning an expected value

We have a coin that has a probability $p>1/2$ of coming up heads (and probability $1-p$ of coming up tails). We now play the following game: We start with a fortune of one dollar. We toss the ...
4
votes
1answer
189 views

Maximizing gambling performance over the long run

Background. We can play a game in which we can put one dollar and get out $X$ dollars, where $X$ is 2 dollars with probability $p>1/2$, or zero dollars with probability $1-p$. We also assume that ...
4
votes
1answer
262 views

How to determine annual payments on a partially repaid loan?

A 10-year loan of $500 is repaid with payments at the end of each year. The lender charges interest at an annual effective rate of 10%. Each of the first ten payments is 150% of the amount ...
3
votes
0answers
147 views

Algorithm/Formula to compute adding and/or removing compound and/or non-compound percentages from a value?

I will first start with a scenario, I have to apply some adjustments to a particular value. These adjustments are either compound or non-compounded and they can either be added or subtracted to the ...
2
votes
1answer
6k views

Finding Revenue Function and Max Revenue

Studying for a midterm. The demand function for a manufacture's product is $p=1000-\frac1{80} q$ Where $p$ is the price (in dollars) per unit when $q$ units are demanded (per week) by consumers. ...
1
vote
1answer
367 views

Determining tax percentage

I'm working a problem, attempting to find a income tax rate that will change depending on the gross paycheck amount. Some data points: $800 gross = 11% taxed $1500 gross = 16% taxed $2000 gross = ...
0
votes
1answer
97 views

Interest Rate Tree in Matlab

I would like to calibrate a interest rate tree using the optimization tool in matlab. Need some guidance on doing it. The interest rate tree looks like this: How it works: 3.73% = 2.5%*exp(2*0.2) ...
0
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1answer
267 views

Why the $Vega$ of the Black Scholes Model is at its maximum for at-the-money options?

In my course script, it is said that the Vega of the Black Scholes Model is at its maximum for at-the-money options. In order to verify this, I did the following calculations: In the Black Scholes ...
0
votes
1answer
86 views

When does variance fail to meet its purpose in mathematical statistics? [closed]

It have shown in a lot of both math and statistics book, however, When the books define the variance, it doesn't give much attention to math based theoretical background, i wonder if some formula that ...
0
votes
1answer
101 views

Binomial expansion for solving american put option identity [duplicate]

For american put option I have to prove that: 1) As $D$ tends to $\infty$, $a_n$ tends to $-r/D$ so that $S^*$ tends to $0$. 2) As $D$ tends to $-\infty$, $a_n$ tends to $2D/ \sigma^2$ so that ...
0
votes
2answers
106 views

How to solve for $i$ and $n$ in compound interest formula?

Given that $$F = A{ (1+i)^n - 1 \over i}$$ How can you solve for $i$ or $n$?