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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Writing $A(t)=1+S_1S_2^{-1}$ as an Ito diffusion process.

Let $W$ be a Wiener process/Brownian motian and let $$ \begin{align} \mathrm{d}S_1 &= 2S_1(t)dt +3S_1(t) dW\\ \mathrm{d}S_2 &= 4S_2(t)dt +5S_2(t) dW \end{align} $$ Now I'd like to write ...
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1answer
60 views

What is the minimum Premium to be asked for a risk X?

Suppose that an insurer has an exponential utility function $u(x) =-2e^{-2x}.$ What is the minimum premium $P^{-}$ to be asked for a risk X? I got some hint for this, but I could not understand ...
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66 views

Need help with partial derivatives

So here's the question: The monthly payment $P$ on a mortgage loan of $A$ dollars at an APR of $r$ (as a decimal) for $t$ years is given by this formula. $$P(A,r,t)$= ...
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37 views

Calculating duration and interest Rate for an investment

I'm trying to build a calculator to determine different Factors for specific Investments. I have a Formula to calculate the Grand Total, but I can't see any way to get either the Duration or the ...
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1answer
80 views

Question about the risk analysis.

In the above one can see the detail of this question, I am beginner in this kind of mathematics. I will be very greatful if any one can help me to solve them.
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2answers
193 views

find the amount of loan, principal and the interest.

A borrower is repaying a loan at 5% effective with payments at the end of each year for 12 years, such that the payment at the end of the first year is 220, at the end of the second year is 210 and so ...
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40 views

What is my interest rate?

Since my bank is not proud enough to display their interest rate on their home page anymore I am struggling to figure this out. I have an escrow account that looked like 639.14 960.77 1282.4 ...
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1answer
28 views

Find $R$ in $ B = \sum_{i=1}^{60}P_i\left(1+R\right)^{60-i} $ given $B$ and $P_1, P_2, …, P_{60}$

I don't have much training in financial math and was unsure of where to start tackling the following... Given a series of payments $P_1, P_2, ..., P_{60}$ which are increasing sporadically from one ...
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1answer
46 views

How to calculate two asset portfolio (problem finding the Population correlation coefficient)

I have two assets: A has an expected value of $12$ % and a standard deviation of $8$%. B has an expected value of $15$ % and a standard deviation of $12$ %. Suppose that we invest $75$ % in A and ...
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1answer
35 views

Find APR with loan balance

Here is the problem: L: original loan amount B: current balance after P periods P: number of periods that have been paid A: period payment **you do not know the number of periods remaining, so ...
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1answer
39 views

Short and long positions of call options

I am on part c), and I want to know: Since I am the seller of this call option, I sold it for 0.44, and the option is worth 1 dollar at expiration. Assuming the buyer wants to make profit he will ...
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36 views

Forward contracts

How do I do this one? I'm assuming it's not as simple as "the initial value is just $50 since thats what the stock sells at"
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21 views

Difference Between Generalized and Alternative Compounded Interest Equations

I am currently studying a chapter called "An Economic Interpretation of e" in my Economics class and we are finding amounts of compounded interest. I am not actually looking for help on the problems ...
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0answers
147 views

Engineering Economics Cash Flow Diagram

I have the following question and solution below. What I don't understand is why is the 100,000 seen as savings/revenue when clearly it is coming out of pocket? Additionally, the monthly loan payment ...
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1answer
36 views

Simple Interest troubling with new formula

I have learn in my school day Simple Interest can be calculated by $PNR/100,$ where $P$ is principle amount, $N$ is number of years and $R$ is rate of interest. For example, if I take$ P = 100, N = ...
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1answer
129 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) ...
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2answers
1k 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 ...
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2answers
65 views

Find percentage increase per period to match a different percentage over the same period

Bob has an account with £1000 that pays 3.5% interest that is fixed for 5 years and he cannot withdraw that money over the 5 years Sue has an account with £1000 that pays 2.25% for one year, and is ...
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56 views

Bonds and zero rates

I don't get how to do this one, is a bond similar to compounding interest?
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1answer
76 views

Asset Depreciation - Logarithms

How many years would it take for the value of a car purchased at 30 000 to fall to 15 000 if it depreciates by 15% in the first year and 12% every year after that? This is not actually graded ...
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1answer
174 views

Formula for compound interest with N withdrawals

I have a calculator that allows users to see how much they need to save per period (month, year, etc) when putting money into a savings account. There are N withdrawals made in the end, with N ranging ...
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1answer
27 views

Financials Maths- Credited Interest

You invest £1,000 in an account for 5 years at 9% pa nominal. How much will you get at the end of the 5 years if the interest is is credited: a) annually; b) 6 monthly; c) 3 monthly; ...
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1answer
68 views

Math / Accounting problem

I have been stuck for over an hour with the following problem. In my textbook the following is written: "Suppose, for example, that Polany Manufacturing Company enters into a long-term lease July 1 ...
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1answer
38 views

finding the optimal decision value for two dependent random events.

I have been struggling with this problem regarding options (bermuda) for some time now. You can exercise this option on two seperate occasions namely at $T_1$ or $T_2$ with a strike price $E$. The ...
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1answer
25 views

Find sweet spot between 'Effect' and 'Resource Consumption'

This question is rather of economical nature. Let's say we have a function $f(x)$ that describes the result of some action depending on the amount of resource used $x$, for example: ...
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1answer
203 views

Text on Probability Theory applied to Actuarial Science

I am a senior undergraduate who has passed the first three actuarial exams on probability (P), financial mathematics (FM), and models for financial economics (MFE). I am working on passing the life ...
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1answer
316 views

Calculating the value of Annuities

Q: Instead of investing $3000$ at the end of $5$ years, and $\$4000$ at the end of $10$ years, Steve wishes to make regular monthly payments that will amount to the same total after $10$ years. ...
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1answer
17 views

Finding the compounding period

The future value of a 200 deposit in an account that earns 6.25% annual interest is $272.71 after 5 years. Determine the compounding period for this investment. This is what I have done: $272.71= ...
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2answers
182 views

Future Values of Annuities

Michelle has decided to invest $3000 at the end of each year for the next five years in a saving account that pays 8% annually, compounded semi-annually. How much is the annuity worth after 5 years? ...
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2answers
159 views

Compound interest problem

Find the present value and accumulated value after 10 years for an income stream with the rate of money flow $f(t) = 200 + 150t$ dollars per year and the rate of interest 12% compounded continously. ...
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1answer
50 views

Price of Product

Suppose an item costs $ \$10$. The expected demand for 4 years are: $$ \text{1st year}: 5$$ $$ \text{2nd year}:10 $$ $$ \text{3rd year}:1 $$ $$ \text{4th year}:2 $$ The actual demand is: $$ ...
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2answers
106 views

Financial Maths question - Calculate number of years over which loan will be repaid

A loan has to be repaid over 3n years, through annual repayment installments of 5000 each at an annual interest rate of 10%. Sum of the Interests paid in the (n+1) and that in the 2n+1 year is 5000. ...
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2answers
284 views

Growth Rate. A precise definition.

Recently I came across a problem (see statement below) growth rate . During my attempts to solve the exercise I concluded that I do not know the meaning of need backup growth rate when this rate is ...
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1answer
70 views

A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints

In Evans and Jovanovic (1989) you will find a model for entrepreneurs with credit constraints. The part that is important for my question follows. Here it is the production function and the income ...
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1answer
132 views

[solved]Compound interest problem

I must admit this is my homework, but I have tried to solve it from many different angles but I can't solve it. The problem is as follows: A person has a 500 dollar debt to be paid in 3 years at an ...
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1answer
114 views

solving apr using binary chop

I need to calculate apr in the uk using this formula http://en.m.wikipedia.org/wiki/Annual_percentage_rate#European_Union Ive been advised to try the binary chop method but I have no idea how to do ...
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1answer
781 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 ...
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1answer
67 views

Find a function that highlights Gamma for short dated fx options and Vega for long dated fx options

I'm new to this and would like to try it out on the above question. A more detailed description is shown below: My professor has asked me to come up with a formula that will highlight, say the 100 ...
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30 views

How to sum correlation, or, calculate correlation of disjointed variables

I'm trying to calculate the correlation of 2 array of variables, but the array is disjointed in the middle - but I'm trying to obtain one correlation coefficient See the excel file I uploaded: ...
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0answers
28 views

Average Interest Payment For Specific Period of Ammortization Schedule

I would like to derive an equation that calculates the average interest payment x for an amortized mortgage loan in the first m ...
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1answer
73 views

Using Ito Formula to compute $E[cos(B_t)]$

During the semester my prof (for a basic Mathematical Finance course) gave us some more challenging type questions to think about if we plan to take future courses on the topic. One of the questions ...
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1answer
49 views

variance unchanged under subtracting mean - application in portfolio theory

I’m working through the following passage: We will be interested in the variance of the portfolio returns given the variances of individual asset’s returns. If we have assets with returns ...
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2answers
52 views

Algebra — Am I doing it right?

Is this correct? $ \frac{1 + 0.05}{1 + x} = \frac{1 + 0.02}{1 + 0.06} $ $\frac{1.05}{1 + x} = \frac{1.02}{1.06} $ $\frac{1.05}{1 + x} = 0.9623 $ $1.05 = 0.9623(1 + x) $ $ \frac{1.05}{0.9623} = ...
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224 views

What does it mean to “pass to the limit” in mathematics?

I've been reading a finance paper and stumbled upon this phrase. What does passing to the limit mean in this context (or overall in mathematics)? Here is an excerpt from the paper: It is ...
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1answer
99 views

Questions on share prices of a Company.

Company Z is currently financed solely by common stock and has 1000 outstanding shares with a (time 0) market price of 10 dollars per share. The company’s expected earnings is 1000 dollarseach year ...
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1answer
130 views

Discounting Perpetuity Question

"A project pays a dividend of $0.75 next year and then grows at 12% for 3 more years, and then grows at 8% indefinitely thereafter, find PV" Okay so first step is to find the initial value of ...
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1answer
57 views

Help me optimize my work

I am a physician. I am required to work 14 shifts per month. I may work extra shifts for 1400 dollars per shift. In addition, I earn productivity based on a system called RVUs. For every RVU I produce ...
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1answer
480 views

compound interest with geometric series

Were studying geometric sequences in maths and this came up as one of the questions: A mortgage is taken out for 150000 and is repaid annually with 20000 installments. Interest is charged on the ...
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2answers
163 views

How to calculate profit share for this example [closed]

How can we calculate a profit share for Rs. 100,000 that remained in an account for 5 days only. See this question illustration below I was confused about which tags were more appropriate for ...
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2answers
520 views

Calculating monthly instalment after down payment

An item is available for $34000\$$ cash or $20000\$$ cash down payment together with $5$ equal monthly instalments. If the rate of interest charged under the instalment plan is $30\%$ per annum, ...