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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7
votes
1answer
712 views

The so-called rule of 72 (or rather, 69)

This BBC article discusses the 'rule of 72' - essentially along the lines that questions to do with economic growth and inflation and so forth can be approximated by a simple formula using the number ...
2
votes
1answer
659 views

Statistics with overlapping periods

I've been having a lot of discussions about finance recently in which people will point to some results using overlapping time periods and claim a high degree of statistical significance. For ...
0
votes
1answer
154 views

Compound interest

I've watched the khan academy pre-calculus playlist about compound interest and constant e on youtube Khan Academy. First he said that you can compute the final payment like this: Let P = Principal, ...
2
votes
2answers
226 views

Bonds and Yield Rate

I came across the following problem on bonds: Suppose we are given the following term structure of annual effective yield rates for zero coupon bonds: $(1, 2 \%)$, $(2, 6 \%)$, $(3, 7 \%)$, and ...
1
vote
2answers
316 views

Problem calculating percentage compound interest

I have two problems: 1. How can i calculate compound interest when i want to reinvest a percentage of the sum of my principal and interest periodically? To make it clearer, Usually i use this ...
3
votes
2answers
521 views

Put Options and Arbitrage

I came across the following problem on put options: A European put with strike price $100$ expiring in $1$ year has premium $ \$ 1$ and a European put with strike price $K$ expiring in $1$ year ...
3
votes
1answer
778 views

What is the definition of a “predictable process”?

I am reading a book on financial mathematics, and frequently encounter the phrase "predictable process", which I haven't seen definition of, and cannot find the definition online. At first I thought ...
2
votes
2answers
136 views

Solve for level payment with a twist

Reworded trying to clarify. Also corrected example to correctly state 4 years and 150 days. I'm struggling with how to solve for a level withdrawal that will reduce a starting balance amount to zero ...
1
vote
1answer
234 views

Binomial model of stock price

I've got a homework question which I think I have solved but am not certain if the answers are correct. The question goes like this: Consider a stock which has a 50% chance of increasing by 80% by the ...
0
votes
1answer
2k views

Money-Weighted and Time-Weighted Rate of Return

I have a question on Time-Weighted Rate of Return (TWRR) and then a question on the links between MWRR and TWRR, An investor invested £100 in a fund on Jan 1st 1998 and another £100 on Jan 1st 1999. ...
0
votes
2answers
1k views

what is running yield?

Suppose an investor who pays £120 on 15 July 2007 for £100 nominal of a six-year stock with half-yearly coupon payments of 13% pa and is not subject to tax. The stock is redeemable at par. Calculate ...
3
votes
2answers
1k views

APR Calculation

I'm hoping someone can clarify this for me. The model/example is this: We lend an amount of 1498.50 (loan amount). Other fees total 39.95. The term of the loan is for 12 months. There is no ...
10
votes
1answer
397 views

A (mathematically) sound investment strategy

It is common wisdom in the investment community that a long-term investor saving for his future would do well to invest in high-risk/high-return assets when he is young, slowly switching his portfolio ...
1
vote
2answers
239 views

Find principal borrowable given monetary deposit, term and monthly payment. With a catch

Edit: I reworded the entire question into an example to make it easier to understand John wants to buy a house. He has €30,000 saved up for a deposit $(D)$ and he know's he can afford to pay €1,200 a ...
0
votes
2answers
225 views

What is wrong with this simple equation?

Consider the following equation: $$\Bigl(\bigl((100 + 5 - 2) * 1.15 + 6\bigr) * (1.07) - 3\Bigr) = 130.1615.$$ I want to take the above and add 3% non-compounded, meaning I want to take 3% of 100 and ...
0
votes
1answer
732 views

recurrence relation on bank interest

Invest 1000 dollars at bank at 3 percent interest compound annually. Every year the bank deducts 15 dollars in charges. If $A_n$ is the value of the investment at the end of $n$ years write down a ...
3
votes
0answers
160 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 ...
0
votes
1answer
156 views

Optimizing Group Spending

I have always thought that groups of individuals that spend more money(as opposed to save) have more money in the long run. My reasoning is that if a particular group spends money, then each dollar ...
1
vote
2answers
525 views

Using Black-Scholes Equation to “buy” stocks

From what I understand, Black-Scholes equation in finance is used to price options which are a contract between a potential buyer and a seller. Can I use this mathematical framework to "buy" a stock? ...
0
votes
1answer
63 views

How Can I Arrive at the Fee-Adjusted APR, Accounting for Balance Transfer Fee (But Not Inflation)?

I'm trying to figure out the fee-adjusted interest rate paid when incurring a balance transfer fee on a loan, not accounting for inflation. If the APR is 4%, the loan 5000, the transfer 2% and you ...
0
votes
2answers
173 views

Interest Calculation Problem

I want to calculate how much I would pay monthly. $X$ = Amount borrowed. $I$= Interest Rate. $Y$ = number of years This is what I have so far, but it's wrong; I'm getting a larger value. ...
0
votes
1answer
884 views

Accounting Question: Computing margin of Safety Ratio

Smith Company produces desk lamps. The information for June indicated that the selling price was $\$25$ per unit, variable costs were $\$15$ per unit, fixed costs totaled $\$6,000$, and the margin of ...
7
votes
5answers
979 views

Paying off a mortgage twice as fast?

My brother has a 30 year fixed mortgage. He pays monthly. Every month my brother doubles his principal payment (so every month, he pays a little bit more, according to how much more principal he's ...
0
votes
1answer
538 views

What is the total inflation rate over a several year period given the each year inflation rate?

Consider a given inflation rates $I_1, I_2, \dots, I_N$ for years $1 \dots N$. What is the total (cumulative) inflation rate over the whole period of $N$ years? I was trying to chain-link the ...
1
vote
1answer
804 views

Solve for n in Compound Interest Formula

I would like to solve the compound interest formula $$V = Pz^n + c\left(\frac{z^{n+1}-z}{z-1}\right)$$ for $n$. Or, given what I would like the final value to be, the amount I can save a year, an ...
1
vote
1answer
1k views

Rewriting Dividend Discount Model to derive residual income model

How can I rewrite this equation: $ \hspace{2in} V_0=\frac{E_1+B_0-B_1}{(1+r)^1} + \frac{E_2+B_1-B_2}{(1+r)^2} + \frac{E_3+B_2-B_3}{1+r)^3} + \dots $ into: $ ...
0
votes
1answer
115 views

Bending algorithm needed

Can someone help me with the formula needed to obtain the following. I need to discount products on a sliding scale. If a customer purchases 2 products, he must get a 15% discount. If he purchases 10, ...
1
vote
1answer
6k views

How to derive Gordon growth model

The formula for the Gordon growth model is: $\hspace{1in}P= \sum_{t=1}^{\infty} D\times\frac{(1+g)^t}{(1+k)^t}$ So summing the infinite series we get: $\hspace{1in}P=\frac{D(1+g)}{k-g} ...
1
vote
2answers
821 views

mortgage math problem

There's a 30 year home loan for $100,000 at 7%. After 15 years the loan is paid off in order to refinance at a lower rate. The loan has a prepayment penalty of six months interest of 80% of the ...
1
vote
0answers
176 views

Immunization and Sensitivity Analysis

Frequently a company wants to match its assets and liabilities. However, perfect matching is not practical due to fluctuations in interest rates. So they hedge their risk using immunization. This can ...
1
vote
0answers
151 views

Dividend Discount Model

The current price of a stock can be modeled by $P_0 = \frac{D_{1}}{r-g}$ where $D_1$ is the expected dividend, $r$ is the rate of return, and $g$ is the expected growth rate in the perpetuity. If ...
1
vote
2answers
362 views

Tricky Finance-related Question

Suppose I have acquired 103,304 customers for a transaction-based business at 12 months into the business and their number has increased at a monthly rate of 40% (from month 1, in which 2,551 ...
1
vote
1answer
195 views

Interest of interest calculations without logarithm

I have some problems understanding a question in a math class test for 10 year olds. The question is: Someone pays in 200€ to a bank. The interest rate is 3.75%. Some time later, he looks at the ...
0
votes
1answer
258 views

Stock/Futures put options

How do you find out how much a put contract would cost? Example: The premium for a 99.00 Eurodollar futures put option is 0.55 and the spot price is 98.51 So I have the intrinsic value which ...
0
votes
3answers
95 views

Annuity immediate

An annuity immediate has quarterly payments of $1000$ for $25$ years at a rate of $6 \%$ converted quarterly. Find its present value. The effective interest rate $i$ is $0.06/4$. So let $v = ...
0
votes
3answers
1k views

Loan Repayment and Annuities

A loan for $50,000$ has level payments to be made at the end of each year for 10 years at an annual rate of $9 \%$. (a) Find the balance at the end of $3$ years. (b) Find the interest paid in the ...
2
votes
1answer
134 views

Payments and Interest Rates

Suppose you have two options for making a payment: (A) Pay $90 \%$ of the purchase price two months after the date of the sale. (B) Deduct $X \%$ off the purchase price and pay cash on the date of ...
0
votes
1answer
667 views

proof that value at risk VaR is monotonic

I want to show that if $X$ and $Y$ are the two loss variables such that $X\leq Y$, then $\text{VaR}_\delta(X)\leq\text{VaR}_\delta(Y)$.
2
votes
1answer
341 views

Derivatives of Brownian motion or Box Options Greeks

Here's the probability (I think) that a particle in Brownian motion (w/ standard deviation $\sqrt{t}$) will exceed $m$ between times $t_1$ and $t_2$: $$\frac1{2\sqrt{2\pi}}\int_{-\infty }^m ...
3
votes
1answer
264 views

Black-Scholes equation

In Stein-Shakarchi's book Fourier Analysis (p. 170), the solution of the Black-Scholes equation $$\frac{\partial V}{\partial t}+rs\frac{\partial V}{\partial s}+\frac{\sigma^2s^2}{2}\frac{\partial^2 ...
0
votes
1answer
585 views

Instalment APR Calculation Formula

I have a problem that I cannot solve regarding interest payments, and payment holidays. The scenario is this If I purchase a product which is paid for over a 12 month period, I need to calculate the ...
6
votes
2answers
833 views

Black Scholes PDE and its many solutions

I know the general Black-Scholes formula for Option pricing theory (for calls and puts), however I want to know the other solutions to the Black-Scholes PDE and its various boundary conditions. Can ...
14
votes
2answers
1k views

Farkas’ lemma: purely algebraic intuition

Here is a statement of Farkas Lemma from the Wikipedia. Let $A$ be an $m \times n$ matrix and $b$ an $m$-dimensional vector. Then, exactly one of the following two statements is true: There exists ...
1
vote
2answers
190 views

Stochastic/finance monte carlo question

When pricing a european option by monte carlo over 30 days for instance, what's the difference between one big 30 day jump vs 30 one day steps?
5
votes
5answers
4k views

Understanding Black-Scholes

Assume I have only basic math knowledge, what specific areas of math would I need to learn in order to understand the following webpage: Black-Scholes Many thanks.
1
vote
2answers
220 views

Principal and Annuities

Suppose you want to accumulate $12,000$ in a $5 \%$ account by making a level deposit at the beginning of each of the next 9 years. Find the required level payment. So this seems to be an annuity due ...
2
votes
1answer
208 views

Annuities and Loans

A loan for $8,000$ must be repaid with 6 year end payments at an annual rate of $11 \%$. What is the annual payment? I know that the present value of an annuity with end payments is $\frac{1-v^n}{i}$ ...
3
votes
2answers
254 views

Measuring Financial Investment Performance

I'm trying to understand how the performance of financial investments are measuring when the asset has multiple points of investment. For example, say I invest ...
2
votes
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 ...
4
votes
1answer
292 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 ...