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
232 views

Calculate interests

Simply wants to calculate interests of an initial amount $N$, with a monthly payback $m$, and a year interest rate of $R$ I guess the interests are not cumulated each month, but just at the end of ...
2
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1answer
6k views

Effective Annual Rate Calculation: Tricky periods and payout frequencies

For calculating the Effective Annual Rate (EAR) from various stated interest rates, I'm using the formula: $$EAR= \left(1+\frac{r}{p}\right)^{pt}-1$$ where, $p$ = no. of payouts in a period, $t$ = ...
2
votes
2answers
661 views

Baseball betting and probablity

Here is a question that came up during class discussions on Friday: Your favorite baseball team is playing against your uncle's favorite team in the World Series. At the beginning of each game, you ...
2
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1answer
31 views

Future Value and Present Value of a General Annuity Due

I understand that a general annuity due, the payments are made at the beginning of each payment period, and the compounding period is not equal to the payment period. Then to solve I need to transform ...
2
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1answer
48 views

continuous local martingale brownian motion

$B$ is a one-dimensional Brownian motion and $X_t$ is defined as$\\$ $X_t:=f_{1-t}(B_t)$, $0\le t<1$ and $0$, $1\le t<\infty$ where $f_s(x)=\frac{1}{\sqrt{2\pi s}}e^{-\frac{x^2}{2s}}$. I have to ...
2
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1answer
41 views

Financial Mathematics problem.

Consider a property developer who buys a property at time $0$ for $\$90,000$. He also spends $\$10,000$ at time $0$ to buy some materials he will use to develop the property. Ignoring Inflation , the ...
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2answers
65 views

Financial Mathematics problem

$i^{(p)}$ is the nominal interest converted p-thly i.e the total interest per unit of time paid on a loan of amount 1 at time 0 where interest paid in p equal installments at the end of each p-th ...
2
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2answers
41 views

Annuity and Loan Repayment Question. Show the amount of Loan.

A loan was taken out on 1 September 1998 and was repayable by the following scheme: The first repayment was made on 1 July 1999 and was £1000. Thereafter, repayments were made on 1 November 1999, 1 ...
2
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1answer
235 views

Calculus in Economics

A company is planning to manufacture and market a new headphone set. After conducting extensive market surveys, the research department provides the following estimates: Marginal costs function: ...
2
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1answer
90 views

Simple vs compound interest rates and Taylor expansion

I am having trouble deciphering a portion from my finance text. Let $i = \text{interest rate}$, $n = \text{Some arbitrary time period}$ and $C = \text{Cash invested}$ And also $C(1+i)^n$ ...
2
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2answers
51 views

Methods of solving this exam FM problem with geometric-investments.

The problem I am working on is as follows. Matthew makes a series of payments at the beginning of each year for $20$ years. The first payment is $100$. Each subsequent payment through the tenth ...
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2answers
80 views

Interest rates. What is the difference between $I=I_0(1+r)^t$ and $\frac{dI}{dt}=rI$?

When I was in school, we used this method for generating the amount of money would be in a bank account after $t$ years with interest rate $r$: $$I=I_0(1+r)^t \text{ where }I_0\text{ is the initial ...
2
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2answers
47 views

Identity of $I_t$ under annuity with principal $1$

I am trying to prove an identity and quite not get there. The following is the premise. One deposits $\$1$ at time $t=1,2, \cdots ,n$. evenly spaced. The effective interest per payment is $i$. ...
2
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2answers
62 views

Vanilla swap payoff

The payoff of a plain vanilla swap with respect to measure $Q$ is : $$V_{\mathrm{swap}}(t) = \beta(t) \sum_{n=0}^{N-1} \tau_n E_t^Q \left( \dfrac{1}{\beta(T_{n+1})} ( L(T_n, T_n, T_{n+1}) - k) ...
2
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1answer
94 views

Math Finance: Arbitragefree Pricing Q vs. P

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if there exists a riskneutral equivalent martingale measure Q~P, under which the discounted asset price ...
2
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2answers
64 views

Solving $a_1x_1 + \cdots +a_nx_n = b$

I'm glad to ask my first question on the maths site! So here we go. I'm trying to set up prices right now and here is my problem : I know that my customer has a certain amount of money available. ...
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2answers
2k views

Calculating inflation rate

This is my maths problem (It is NOT homework help, just me trying to learn basics of this bit of maths): A car cost £14,000 in May 1994, the inflation rate then was 1.9%, but the current inflation ...
2
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1answer
58 views

Trying to calculate FV with annual & monthly fees

First question on here so please go easy if it's a stupid one! I have created a PHP based FV calculator for use on a client's website. This is the scenario: They offer returns of ...
2
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2answers
318 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 ...
2
votes
1answer
201 views

Variance Covariance Matrix, positive definiteness

Suppose we have a variance covariance matrix $\Sigma$. Under what conditions on the variance covariance matrix, $\Sigma$ is positive definite, that is $\forall w \neq 0, w^T \Sigma w>0$. In fact, ...
2
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2answers
188 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 ...
2
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1answer
425 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
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2answers
161 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 ...
2
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2answers
11k views

How the formula for EMI is derived

I was looking for a formula to calculate EMI (Equated Monthly Installments). I have some fixed known parameters like, Principal Amount, Rate of Interest and No. Of Installments. By googling, I came ...
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2answers
154 views

Compounding with varying principal?

The question pertains to determining average rate of return per year over $n$ years when the final amount and principal invested each year is known and it is assumed that the principal is invested at ...
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2answers
996 views

Daily rate loan APR

This example comes from used car software that is approved in Texas, a state which calculates interest using a true daily earnings method (definition below): The terms are: Amount financed: 5,000 ...
2
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1answer
968 views

Converting an Annuity due to Annuity immediate

I'm working on the following problem at the moment while preparing for an exam. Find the present value of payments of 200 every six months starting immediately and continuing through four years from ...
2
votes
1answer
855 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 ...
2
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1answer
135 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 ...
2
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1answer
215 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 $\frac{1-v^n}{i}$ ...
2
votes
1answer
31 views

Buyer's price in terms of risk-neutral measures

Let us consider a finite arbitrage-free market model $(B,S)$, where $B$ is a bank account and $S$ is a share. Let $X$ be a claim. We define a buyer's price of $X$ as follows:$$\Pi^b_0(X)=\sup \lbrace ...
2
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1answer
24 views

Get rate from Future Value of Annuity

$FV = \dfrac{(1+i)^t-1}{i}\cdot C$ What are the algabraic steps I need to rearrange to get i? The i divided by the i is specifically tripping me up. Many thanks!
2
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1answer
34 views

Is this the correct continous compounding equivalent to daily compunding of 90%?

Find the rate of continuous compounding equivalent to daily compounding of 90%, if we assume that a year has 365 days. P=principle daily = $P(1+(\frac{0.9}{365}))^{365}$ continuous = $Pe^x$ ...
2
votes
1answer
50 views

HJM model - Differentiation Problem

starting from the folowing SDE (HJM model): $$df(t,T)=\left(\sigma(t,T)'\int_t^T{\sigma(t,u)du}\right)dt+\sigma(t,T)'dW_t$$ And having $r(t)=f(t,t)$, I have two questions : 1) how do we obtain the ...
2
votes
1answer
41 views

Pricing a Europen style put option

So I'm enrolled in a Mathematics for Finance course, and we received this question on the last Problem Set. I'm completely stuck on how to solve this problem. I tried applying the formula xS(t) + ...
2
votes
1answer
38 views

Clarification on a collared stock being equivalent to a bull spread?

The following is a question on financial math from the financial math actuarial exam: Earlier in the manual, the author stated that a collared stock is equivalent to a bull spread. Therefore, in ...
2
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2answers
50 views

To mark up in retail by $20$%, do I add $0.20$ times the original cost, or divide by $0.80$?

Why is it that when I take a cost of say $\$15.60$ and want to mark the item up at retail 20% that I'm being told two different ways with two different answers? The first way (my way) would be to ...
2
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1answer
110 views

Savings account interest rate

Just a brief question regarding bank interest rates, my apologies if this is a duplicate, I did a quick search but came up with no results relating to my question, surprisingly. Also, please excuse ...
2
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1answer
318 views

Market Making Card Bet Game

In an interview I received the follow question: We have 3 cards face down, and we give each card in a deck of 52 a numeric score ( A = 1, 2=2, .... , J=11, Q=12, K = 13). The interviewer asked me to ...
2
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2answers
115 views

Simple Interest Problem Ambiguity in Conventions

I am solving some simple interest problems. Following questions are creating ambiguity with conventions, hope someone will clarify what is going on. In what time does sum of money become 4 times ...
2
votes
1answer
54 views

CI for the expected value of the sum of two dependent normal RVs

Let's consider 2 dependent, normally distributed R.V.s, $X_1$ and $X_2$. The means, $\mu_1$ and $\mu_2$ are known, as well the covariance matrix $\Sigma$. Let's consider the following random ...
2
votes
1answer
205 views

Annuity problem, calculating the accumulated value.

the following is the problem I am trying to work on. Kathryn deposits 100 into an account at the beggining of each 4 year period for 40 years. The account credits interest at an effective annual ...
2
votes
1answer
70 views

Intuitive understanging of re-investment.

There was an interesting problem that I would like to have some input from people who knows a bit of finance. The following is the situation. Smith loans $\$10,000$ for $i=5\%$ for $10$ years. ...
2
votes
1answer
74 views

On estimating monthly credit card payment amounts (some pragmatic constraints inside)

Right off the bat, I do hope this question doesn't attract a bunch of derisive comments about my personal affairs. I give the lengthy personal anecdote because I don't have the mathematical training ...
2
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2answers
39 views

Question about a summation problem from finance

I'm studying a journal article about finance and I have trouble understanding how the author reach a result. The equation he begins with is: $$VTS_0=TD_0+T\Sigma_1^\infty PV_0[ΔD_t] \tag 1$$ Then ...
2
votes
1answer
49 views

Method to calculate the best way to repay two different loans given a set amount of money per month?

Given two (or more) loans of different balances and interest rates and a single amount of funds available per payment period, is there a way to calculate the best way to split the available funds to ...
2
votes
1answer
45 views

Arbitrage opportunity for call price set on avarage

I have the following problem. Let C(K) be the market price of a Option Call with respect to the strike K. Let $C(100) = \frac{C(110)+C(90)}{2}$, then show that there exists an arbitrage opportunity. ...
2
votes
1answer
59 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 ...
2
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1answer
86 views

Optimal Investment Strategy

I am not sure to solve the following investment problem: I have an investor which receives an income $I_n\ge 0$ at the start of year $n$. The investor chooses a proportion $p_n\in[0,1]$ of this in ...
2
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2answers
54 views

Working out the difference in earnings

I'm mathematically impaired/ignorant and trying to figure out the difference in earnings between my partner and I to work out a fair split of the bills. So; I earn £2060 per month and partner earns ...