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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1answer
62 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 ...
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2answers
167 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. ...
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1answer
804 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
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5answers
828 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 ...
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1answer
455 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 ...
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1answer
673 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 ...
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1answer
954 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
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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, ...
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1answer
5k 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} ...
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2answers
727 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 ...
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0answers
162 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 ...
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0answers
145 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
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2answers
337 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
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1answer
187 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 ...
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1answer
250 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
85 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 = ...
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votes
3answers
880 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
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1answer
129 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
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1answer
559 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
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1answer
334 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 ...
2
votes
1answer
247 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
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1answer
515 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
757 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 ...
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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 ...
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2answers
186 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?
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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
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2answers
206 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
193 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
245 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
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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 ...
4
votes
1answer
270 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 ...