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

learn more… | top users | synonyms

1
vote
1answer
58 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
1k 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
92 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
314 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
170 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 ...
-1
votes
1answer
101 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
285 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
41 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
149 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
116 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
329 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
76 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
105 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
111 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
66 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
118 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
144 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
58 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
37 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
272 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
45 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
91 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
232 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
181 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
59 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
228 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
155 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
255 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
254 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 ...
2
votes
4answers
13k 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
206 views

Find the accumulated value of an investment fund

Find the accumulated value at the end of six years of an investment fund in which \$100 is deposited at the beginning of each quarter for the first three years and \$50 is deposited at the beginning ...
0
votes
1answer
50 views

Find the relative shares of B,C and D in the estate, if it is assumed that the estate will earn a 7% annual eff

Person A leaves an estate of $100,000. Interest on the estate is paid at the end of the year to beneficiary B for the first 10 years, to beneficiary C for the next 10 years, and to charity D ...
2
votes
1answer
158 views

Is the following a martingale?

Let $X_{n}$ be a martingale with respect to a filtration $\mathbb{P}_{n}$. Define: $Y_{n}$ := $X_{n}^{3}$ Is $Y_{n}$ a martingale? Supermartingale?
2
votes
0answers
89 views

Doob Decomposition of American Option

I am trying to figure out the Doob decomposition of an American put option in a discrete time binomial model. I know how to price the American put, but I'm having trouble expressing it as the sum of ...
0
votes
3answers
150 views

A fund of $30,000 is used to award scholarships…If i=0.09, find the number of scholarships which can be awarded

A fund of $30,000 is used to award scholarships of amount 3000, one per year, at the end of each year for as long as possible. If i=0.09, find the number of scholarships which can be awarded and the ...
0
votes
2answers
62 views

If $ i=0.09 $, find $ n $ and the amount of final payment.

A fund of $ \$500 $ is to be accumulated by $ n $ annual payments of $ \$100 $, plus a final payment as small as possible made one year after the last regular payment. If $ i = 0.09 $, find $ n $ and ...
1
vote
2answers
259 views

at a nominal rate of interest of 8% converted semiannually…Find the initial amount of the loan.

A loan is to be repaid with level instalments payable at the end of each half-year for $3$ and $\frac{1}{2}$ years, at a nominal rate of interest of 8% converted semiannually. After the $4^{\rm th}$ ...
1
vote
1answer
588 views

Determine the effective annual interest rate on the loan

A borrower owes \$5000 today and has promised to pay \$1900 at the end of the next three years to repay the loan. Determine the effective annual interest rate on the loan. What is the outstanding ...
0
votes
2answers
328 views

Determine the monthly payments if the nominal rate is 12% converted monthly

a) A $\$50,000$ mortgage is to be repaid by monthly payments for $20$ years. Determine the monthly payments if the nominal rate is $12\%$ converted monthly b) an extra payment of $\$1,000$ is made at ...
0
votes
2answers
230 views

Why does the internal rate of return have no analytic expression?

I know that the IRR can be computed using iterative methods, but why is this necessary? What makes it impossible to give an expression for IRR? How would you prove it to be impossible?
1
vote
2answers
325 views

Profit and Loss calculation: Fake currency

A store buys an item for $\$50$. They price it then, at $\$80$ ($\$30$ profit margin). A customer buys the item from them with a fake $\$100$ note. The store returns $\$20$ to the customer. My ...