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
99 views

How to split the rent if two roommates live there from the beginning and a third one joins in the middle of the month?

I've been thinking over it and I can't figure it out. Consider the rent of the house is $X$. Now there are two roommates from the beginning and a third one joins in the middle of the month. Now ...
0
votes
1answer
79 views

Interest Calculation

A university student receives his statement for his tuition and notices that he doesn't have enough money to pay it all off at once. The student inquires about interest rates at his university and is ...
1
vote
1answer
33 views

Mortgage calculating time for residual debt

I have a mortgage for C capital, with constant monthly payments, constant interest rate i (and constant duration in year D). I would like to know after how much time I reimburse $r$ dollars. For ...
1
vote
4answers
10k views

No-Arbitrage Principle

I hope you do not mind me asking a financial question in this section. I am having trouble understanding the concept of the no-arbitrage principle for a particular example in my notes: Suppose a ...
3
votes
0answers
97 views

How to get interest in the mathematics of tax

In a similar vein to my previous thread, I will also be teaching about the mathematics behind taxation - to a lot of people, this is very mundane - but that is not true of everyone. The practicality ...
0
votes
1answer
84 views

Portfolio which replicates given payoff

Consider the following payoff function: $$p(S_T) = \begin{cases} 0 & \text{if } S_{T} \leq 70 \\ S_{T}-70 & \text{if } S_{T} \in (70; 100] \\ -S_{T}+120 & \text{if } S_{T} \in (100; 120] ...
0
votes
2answers
82 views

Mathematical Finance Question

I am having trouble answering this question confidently. A walk through would be amazing.
1
vote
1answer
214 views

Calculate the yield rate on transaction

Problem:- 'A' is able to borrow $1000 from 'B' for one year at 8% effective and at the same time lend it to 'C' for one year at 10% effective. what is 'A's yield rate on this transaction? My ...
4
votes
2answers
184 views

Speculating on the stock exchange

Imagine you model each stock as a random walk (fractal) and also that you can buy and sell at any price. Suppose also that it 'walks' with the pace of 1. If you buy, for example, 1000 shares of ...
1
vote
1answer
185 views

Hedging a long position-one period

Consider a one period binomial stock model with $S_0=4$, $S_1(H)=8$ and $S_1(T)=2$. The interest rate is $25$%. Let's say I buy a call option for $1.20$ with strike price $K=5$ which expires at time ...
2
votes
1answer
1k views

Black-Scholes PDE to heat equation, nonconstant coefficients

Can someone provide me with details or a reference on how to transform the Black-Scholes PDE with nonconstant coefficients (i.e. $r=r\left(S,t\right)$, $\sigma=\sigma\left(S,t\right)$) to the heat ...
0
votes
3answers
175 views

$1500=P \times { (1 + 0.02) }^{ 24 }$, what is the value of $P$?

Hey guys could you please tell me what is the faster why to solve this equation. It's a compound interest equation and I'm stuck at the ${ (1 + 0.02) }^{ 24 }$ I really don't know how to proceed in ...
1
vote
1answer
59 views

I'm looking a compound interest formula.

Admittedly, I just finished physics and calculas but some of my more basic math skills escape me. I'm looking for a formula that will give me a total compounded value after x number of weeks. So for ...
1
vote
1answer
1k views

Easy proof of Black-Scholes option pricing formula

I use this Book to read the option princing in Black-Scholes model in pages 93-99, The poof of the formula given by $$c(s,t)= N(d_1(s,t)- Ke^{-rT}N(d_2(s,t)))$$ where $$d_{1,2}=\frac{\ln(s/K)+(r\pm ...
1
vote
2answers
2k views

Calculating interest rate of car financing

I want a new car which costs $\$26.000$. But there's an offer to finance the car: Immediate prepayment: $25\%$ of the original price The amount left is financed with a loan: Duration: $5$ years, ...
0
votes
1answer
2k views

Difference between Bi-annual and semi-annual in Financial Maths

I was wandering what the difference was between compounding interest when they use bi-annual and semi-annual and hence how to change your value of i I think semi-annual means twice in 1 year so your ...
0
votes
1answer
74 views

Early-exercise point of American Put

Could you please help me? In book Rüdiger Seydel "Tools for Computational Finance" in Chapter 4.5 "American Options as Free Boundary Problem" it is provided the following explanation for case ...
1
vote
1answer
95 views

Deferred Annuity not working

A simple financial math problem: Mack obtains $500\ 000$ repayable over $20$ years. If interest is compounded monthly at $9.25\%$ per annum, determine the monthly repayments if the repayment ...
1
vote
0answers
372 views

Notation in Financial Math

I am very close to showing part b of this question and think that the reason my solution doesn't match up is because I don't understand a piece of notation.The notation I don't understand is ...
5
votes
1answer
187 views

Arbitrage opportunity

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 ...
-1
votes
2answers
72 views

How to find the amount to added every month or year to get the required amount after certain years?

I want to do a Java application for which after giving the current savings, and the rate of interest and and required amount after specified no of years, it has to show how much a person has to earn ...
0
votes
1answer
105 views

Why are call options necessary?

My question is actually less ambitious and more specific then the title may have lead you to believe. Suppose the interest rate is $25\%$ you have a stock at time zero price of $S_0=50$ and at time 1 ...
1
vote
1answer
340 views

if you invest $ 500 at 6 % compounded annually,

Please help me with this problem. It needs to be done in the same format as below if you invest $500$ dollars at $6$ percent compounded annually, how many years to the nearest tenth would it take your ...
0
votes
1answer
45 views

Suppose you invest \$10 at 10.2% per annum compounded annually. How many years would it take for your investment to grow to \$15 000?

I'am solving a simlar equation to this and just trying to figure out how they did it? the only part I don't understand is how they got the number.... 1.102 15000 = 10(1.102)n ¬1 mark 1500 = 1.102n
2
votes
1answer
80 views

first order differential question

Mr. John want to buy a house and he must borrow $150,000 from the bank. He wants a 30-year mortgage and he has 2 choice. Choice #1, he can borrow money at 7% per year with no point ( each point is ...
2
votes
2answers
159 views

Probability related finance question: Need a more formal solution

You are offered a contract on a piece of land which is worth $1,000,000$ USD $70\%$ of the time, $500,000$ USD $20\%$ percent of the time, and $150,000$ USD $10\%$ of the time. We're trying to max ...
1
vote
1answer
48 views

Can anyone show me how this was derived?

So here is all the slide says and I'm and trying to see the steps for derivation. Can someone please show me how this is derived? Essentially I'm trying to go from 1 to 2. Pi is the profit function. ...
4
votes
1answer
121 views

Calculating interest rate for a payment plan

I really should know this from high school so I'm a bit ashamed to ask... :) I've been offered several cars for lease and want to compare the offered interest rates. E.g. I have: ...
2
votes
5answers
355 views

Game Theory Question about Financial Markets

This is a recent quote from one of the outstanding bond portfolio managers: "First of all, for every buyer there is a seller. Therefore, in order for someone to sell their bonds and buy stocks means ...
0
votes
1answer
84 views

Find the transaction cost-adjusted expected return of the stock

Let $W^b_i$ denote the weight of stock i in the existing portfolio and $W^a_i$ denote the weight of stock i in the new portfolio to be created. Let $c_i$ denote the transaction cost of stock $i$. If ...
2
votes
0answers
39 views

Stochastic control, numerical, need expectations given coupled SDEs

I'm looking at a trio of processes which arises in a stochastic control situation. I have a process $(V_t)$ which I may control, and $(V_t)$ influences a diffusive stock price process $(S_t)$. The ...
1
vote
3answers
113 views

If you invest $\$1500$ at $7\%$ compounded annually, how many years would it take for your investment to grow

If you invest $\$1500$ at $7\%$ compounded annually, how many years would it take for your investment to grow to $3750$? Is this right? $$\text{term } = \frac{\log( \text{overall gain factor})}{ ...
0
votes
1answer
120 views

confusing part to basic accounting question

Directions: Given the information find the weekly and monthly taxable wages (4.3 weeks per month). This is for federal income taxes. Weekly Taxable Wages: $\$21.40$ per hour, $40$ hours a week, $47$ ...
0
votes
1answer
67 views

How to Maximise Efficiency With hp12c gold calculator: Equation of Value Loan Schedule

I would like to calculate the net present value of a loan schedule or an equation of value. e.g. "For an investor receives R1 000 after 2 years, R2 000 after 5 years and R4000 after 7 years, how much ...
0
votes
1answer
120 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 ...
1
vote
1answer
149 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 ...
2
votes
1answer
60 views

Financial Bonds 500 $1,000 bonds with stated rate of 5% issued at par. 10 year term and pay interest semi-annually.

Every time I try and calculate this problem something comes up wrong. Either from working it out by hand or using my BA II plus, I cannot get the answer shown below. Am I wrong or is this book answer ...
1
vote
2answers
24 views

In this situation, how to decrease the payout amount based on the “weighed” constituent parts?

Couldn't think of a better way to explain it in the title, my bad. This is a problem I'm running into in a programming project. Here's the situation: Say a partner is due to be paid $1000 for ...
0
votes
1answer
38 views

How to find breakeven amount when the buy and sell amount has a fee?

With currency exchange they charge 3% when I buy a currency. When I sell they charge 3% on the amount I sell. My question: At which amount do I need to sell to make up for the 3% fees? I currently ...
2
votes
1answer
292 views

Bonds and Force of Interest

Studying for FM/2 and ran into this problem dealing with bonds; A 1,000 par value 3 year bond with annual coupons of 50 for the first year, 70 for the second year, and 90 for the third year is bought ...
2
votes
1answer
47 views

Calculating percentage reduction from results only.

I've been looking over some loan repayment statements, and I'm trying to work out: What the precentage interest is per month. How long it will be until the final amount reaches 0. Whether there is ...
0
votes
1answer
101 views

Calculate the time after which Money doubles

I while solving a problem in banking just thought to form a formula for the time period after which money deposited in bank at a compounded interest rate @$\alpha $ % p.a. . Amount for compounded ...
1
vote
1answer
2k views

Increasing and decreasing annuity

Going in circles..... Find an expression for the present value of an annuity-immediate where payments start at 1, increase by 1 each period up to a payment of $n$, and then decrease by 1 each period ...
1
vote
1answer
247 views

Continuous annuity calculation

This is a problem from Marcel Finan's Exam FM/2 course. It is not homework but I am studying for the FM exam and trying to get through this. You are given $\frac{d}{dt}\bar{s}_t$ = $(1.02)^{2t}$. ...
0
votes
1answer
200 views

Random Stock Stop-Loss/Stop

Assuming a Stock's price changes in a random manner. If you buy this Stock, you are required to set a stop-return and stop-loss price. I am looking for the equation that shows the probability for ...
0
votes
1answer
66 views

Bond worth given yield to maturity

On 18 February 2010, the bonds were issued with a face value of $\$1,000$. The bonds mature in 15 April 2015 and have an annual coupon rate of $6\%$. (a) Assuming today is 15 April 2013, how much is ...
1
vote
1answer
235 views

A loan is being repaid by 12 annual payments of 3000…determine the principal and interest portions of the tenth payment

A loan is being repaid by 12 annual payments of 3000 followed by 8 annual payments of 5000. If i=0.10, determine the principal and interest portions of the tenth payment and the 15th payment. I am ...
2
votes
2answers
159 views

Are there constraint problem calculators?

So I just remembered Lincoln Logs exist, so I found ten giant sets of them on ebay for Buy It Now, and I'm trying to decide what combination of purchases gives me the most logs for the least money if ...
1
vote
2answers
287 views

Calculating the same exchange rate to make an investor indifferent

If we consider an American investor in 2009 with 160 million Dollars to place in a bank deposit in either America or the UK. The (1 yr) interest rate on bank deposits is 6 percent in the UK and 1 ...
1
vote
1answer
280 views

Find the present value of a ten-year annuity

Find the present value of a ten-year annuity which pays $400$ at the beginning of each quarter for the first $5$ years, increasing to $\$600$ per quarter thereafter. The annual effective rate of ...