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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32 views

How do I find the rate (r) when I only have the Payment (Pmt), term (t) and financed amount (p)?

I know the simple interest formula is, $I = prt$, but I don't know the interest to be able to use that formula. Here's the variables. Please help me with the formula. $$p = \$92,000.00$$ $$t = 72 ...
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1answer
30 views

Covariance of a stock portfolio

I need to find the covariance of two stocks in a portfolio. I know you can calculate covariance as: cov = 1/(n-1)[(summation:Xi-(mean of X))*(summation:Yi-(mean of Y))] However, I don't think I can ...
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2answers
22 views

How do I isolate for the interest with either the the future value or present value equations?

I'm having troubles understanding how to isolate for the interest with either the future value or present value equations. Say we know what $K$ and $n$ are, and I'm trying to find $j$: ...
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2answers
51 views

How to solve $c_1x+c_2x^2+…+c_nx^n = K $ type equation (internal rate of return)

I'm trying to calculate internal rate of return and wonder how you would solve this equation $50x + 20 x^2+75x^3 = 135.6$ The answer is $x = 0.9694$ But does anyone know how to do this ...
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0answers
17 views

Why we need either nonnegative or integrable random variable for the definition of Conditional Expectations

In definition of Measurability and Partial Averaging, it states that: Let (Omega, F, P) be a probability space, let G be a sub-sigma-algebra of F, and let X be a random variable that is either ...
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1answer
20 views

Determining outstanding balance on a loan

A loan of $17,000$ dollars is to be repaid in annual installments of $2,100$ dollars, the first due in one year, followed by a final smaller payment. If the effective rate of interest is $8.8$ ...
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15 views

The question about linked internal rate of return ( Financial Maths)

The performance of an investment fund is to be evaluated over a two year period starting from 1st of January 2008. The given fund had a value of £5.81 mil on the 1st of January 2008 that had ...
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19 views

intro to econometrics in matrix notation

Hi every users of mathstackexchange, each of you are making a lot of contribution to others' knowledge of mathematics and math-related fields. My question would be related to econometrics. This year, ...
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1answer
45 views

Balance after partial payments according to terms [closed]

The Ski Shop received an invoice for $\$9600$ dated August 11, terms $5/10$, $2/30$, $n/90$, for the shipment of skis. The Ski Shop made two partial payments. a) How much was paid on August 20th to ...
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0answers
12 views

Financial Mathematics Dollar-weighted yield

Your grandmother gives you $2800 for your birthday, which you invest in a mutual fund on January 1. On June 1, your fund balance is 7600, and you then deposit 1500 (which you received for your high ...
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1answer
20 views

Finding GST Amount from GST Inclusive Price In New Zealand

In New Zealand, GST (Goods and Services Tax) is equal to 15%. The following formula can be used to work out the GST Amount from the GST Inclusive Price: GST-Inclusive-Price X 3 ÷ 23 = ...
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0answers
73 views

Why predictable processes?

So far I have seen two approaches for a theory of stochastic integration, both based on $L^2$-arguments and approximations. One dealt with a standard Brownian motion as the only possible integrator ...
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0answers
27 views

financial math of bond

a $10000 bond has semiannual interest payments, an annual coupon rate of 4.6%, and an annul yield to maturity - in 4 years - of 5%. If a coupon has just been redeemed, the market price of the bond is: ...
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0answers
27 views

Calculation of bond's market price

A bond \$100 has semiannual coupons worth \$1.30 each (annual coupon rate is 2.6%), matures in 8 years, and yields 3% annually. What is its market price? I think it is $P=100(1.03)^{-8} ...
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1answer
33 views

Expectations and Moments Variance

Suppose $E[X|Y=y] = a + by$ and $V[X|Y=y] = C + dy^2$ where $Y$ is normally distributed with mean μ and variance $σ^2$ . What is $V[X]$?
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22 views

Expectations and Moments

Suppose you invest 10000 in a fund which has expected value of 30000 in two years with a standard deviation of 2000. What can you say about the probability the portfolio value falls between 20000 and ...
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1answer
47 views

Brownian motion / ito's formula

Little help is needed Can I use geometric Brownian motion here? The question I get: $Let z=(z_t)$ be a one-dimensional standard Brownian motion and define the process $y = ( y_t )$ by $y_t = z_t^2 − ...
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0answers
20 views

How to connect a minimum variance portfolio to the Two Fund Theorem using Lagrange?

I've received this question for my Mathematics course at school, and I'm completely stumped as to how we should approach it. I'm unsure how to use the information about a minimum variance portfolio, ...
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1answer
17 views

Annuities-calculating interest

Janet receives a $ 10,000 life insurance benefit. If she uses the proceeds to buy an n-year annuity immediate, the annual payout will be 1613.36. If a 2n-year annuity due is purchased, the annual ...
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10 views

Perpetuity Funding

Alex Rodriguez recently signed a contract with the Texas Rangers that will pay him approximately 250 million dollars over the next 10 years. In this problem, assume that he will receive his pay ...
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0answers
25 views

Covariance of two stochastic integrals

Consider the stochastic integral $\int_{0}^{1}J(r)M(r,\lambda) dr$ where $J(r)$ is a demeaned Ornstein-Uhlenbeck process and $M(r,\lambda)=W(r,\lambda)-\lambda W(r,1)$ a Brownian Sheet, independent of ...
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2answers
25 views

how to calculate compound interest when year is not whole?

The formula for compound interest is Annual Compound Interest Formula: $$A = P\left(1+\frac{r}{n}\right)^{nt}$$ Here year is a whole number. So how can I calculate compound interest on 40,000 for ...
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1answer
23 views

About the denominator in the future value formula

To get the present value of a stock that gives divined in the future we use the formula: P = Div+P1/1+r with P1 is the selling price of the stock after a period. So it's considering what you can get ...
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1answer
45 views

Solving a system of equations - minimizing f

Completely stumped as to how to solve this problem -_- We'd appreciate any help at all: Suppose $f(x, y) = 2x^2 + 2xy + y^2$ and $g(x, y) = x^2 + y^2$ Show that minimizing $f$ with a constraint on ...
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1answer
48 views

Finding an approximation for $E[Y ] − e^{\mu}$?

I don't understand why $E[Y]$ approaches to $e^{\mu}$, and why $E[Y] - e^{\mu}$ is not just zero... Can someone please help me with this problem? Suppose $X$ is normal with mean $\mu$ and variance ...
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0answers
24 views

Solving a Stochastic PDE with two variables in time

I am trying to work on exercise 5.13 in the book Arbitrage Theory in Continuous time by Thomas Bjork. The equation to solve is; \begin{eqnarray*} \frac{\partial F}{\partial t} (t,x,y) + \frac{1}{2} ...
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1answer
170 views

Question about creating $2\times 2$ covariance matrix with call option?

I'm completely stuck on how to do this problem. How can you go about calculating the variance of $Y$ and the covariance between $X$ and $Y$? I'm not sure how to use the information given to solve this ...
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0answers
50 views

Value at Risk, Confidence level, infimum

Given an uncertain future loss L which is modelled as a random variable with cdf Fl , the value at risk (VaR) at confidence level α is defined as $VaR_\alpha (L) = \inf\{l \in R | Fl(l) \ge \alpha\}$. ...
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1answer
67 views

Put and Call options, Financial derivative [closed]

Market Prices for European put and call options on ABC stock are as below: C0 = $4.5 P0 = $6.8 Exercise Price, X =$70 Risk Free Annual Compounded rate r = 5% Time to expiration T = 139 days ...
0
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1answer
43 views

how much is invested at each rate?

The co-operative trust fund is P500,000. Part of the fund is invested at an annual interest rate of 6% and the rest is invested at an annual interest rate of 8%. If the income from both investments is ...
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1answer
25 views

How to Calculate an Import to Receive considering Fees.

I have a problem: I want to receive a sum but, to receive that sum, I have to pay a percentual fee on this transaction. For example: if I want to receive 20 and fee is 10%, I can't require 20 + 10% ...
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0answers
17 views

Orthogonalization of two N dimensional signals as a similarity check

I'm trying to find how 'similar' or 'different' two vectors are, in relation to a third vector. Say A and B are features in my data set, with C being the output. I have N data points for each of them ...
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1answer
20 views

Financial Math, convertible quarterly with multiple cash flows [closed]

On April 1, 2006 Francine opened a savings account paying $9.2\%$ convertible quarterly with a deposit of $\$4500$. On October 1, 2007, she withdrew $\$2400$. On July 1, 2008, she deposited $\$3000$. ...
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1answer
8 views

A problem involving compound interest and a system of equations

Kelly and Justin each win monetary prizes on the TV show US Icon. Kelly immediately deposits her money in an account paying 6.7% effective annual interest, while Justin immediately deposits his in an ...
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1answer
23 views

How to calculate total liabilities?

Columbia Company began the current year with 450,000 in assets and 250,000 in total stockholders equity. During the year Columbia earned 85,000 and distributed 10,000 as dividends. Assets at year ...
0
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1answer
32 views

How to calculate higher monthly payment on term loan such that the last X months are paid at term minimum amount?

This one requires some explanation. What I want to do is calculate how much total monthly payment I would have to pay for x number of months on a loan to get the total balance down to where the loan ...
0
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1answer
36 views

Accumulated value of force of interest

For the period from time 0 to time 2, the force of interest is defined as follows: $$\text{force of interest at }(t) = \begin{cases} 0.05 & 0 \lt t \le 1\\ 0.05+0.02(t-1) & 1\lt t \le 2 ...
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1answer
22 views

Finding effective annual interest rate

I'm working on the question: Bob is beginning his work life and intends to retire in 40 years. He decides to pay 400 dollars at the end of each month into a retirement savings account for the next 40 ...
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2answers
13 views

Perpetual Annuity

I'm working on the question: A benefactor wishes to endow in perpetuity, five annual scholarships of $5,000 at a university. What is the minimum amount she must invest at an annual interest rate of ...
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0answers
8 views

computing $\gamma$ and $\mu$ at the efficient frontier

Consider the condition which the weights of any portfolio belonging to the efficient frontier satisfy: \begin{equation} \gamma\boldsymbol{wC} = \boldsymbol{m} - \mu\boldsymbol{u}\end{equation} ...
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1answer
21 views

Evaluating differing perpetuity payments

A perpetuity pays 1900 dollars on January 1 of 1980, 1982, 1984, ..., and pays X dollars on January 1 of 1981, 1983, 1985, ... If the present value on January 1, 1975 is 26500 dollars, and the ...
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1answer
23 views

Determining interest rates when comparing offers

Option 1: $ 0 down, $ 424 in 1 year , $ 300 in 2 years Option 2: $ 80 down, $ 245 in 1 year , $ 400 in 2 years Determine the range of interest rates for which the present value of Option 2 is ...
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1answer
24 views

What exactly is the meaning of future value/present value of an annuity?

We've been dealing with the idea of annuities in a math course I'm taking, and the idea of "present value" and "future value" have come up. So basically, the "value" of an annuity before someone makes ...
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1answer
37 views

Book recommendations for learning financial/business mathematics.

Does anyone know a book which covers topics on: Simple interest Compound interest Equations of equivalent values Nominal rate, effective rate and equivalent rate Annuities ...
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55 views

Using Generalized Gauss-Laguerre Quadrature

Motivated by the paper "Analytically Pricing European-Style Options Under the Modified Black-Scholes Equation with a Spatial-Fractioonal Derivative", I am trying to use the Generalized Gauss-Laguerre ...
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0answers
25 views

A property of Piece-wise continuous simple linear regression model

My fellow members I attempted to model the growth of capital of a small business person who does business with the aim of just raising his or her capital, as follows: Assumptions A fixed capital ...
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0answers
113 views

How do I calculate compound interest in a reverse interest situation?

I found the following formula that seems to work really well for calculating compound interest when provided a principal amount alongside regularly scheduled additional deposits: ...
2
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1answer
31 views

Risk Neutral Pricing

I'm studying risk neutral pricing and there's a thing I'm not understanding... Let S be a process with the sequent dynamic $\frac{dS}{S}= \mu dt + \sigma dW^P$ where $P$ is the phisical probability. ...
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0answers
33 views

Calculating remaining balance [Monthly compounding question with rate= 0.01]

Suzanne opens a line of credit at a local bank, and immediately borrows 1870 dollars. 6 months later, she repays 1060 dollars. 5 months after the repayment, she borrows 570 more dollars. 6 months ...
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2answers
193 views

How to calculate interest rate given principal initial amount, future value amount, term with monthly contribution

I want to know how to apply a sequence of steps in a program with any mainstream programming language (like Ruby, Java, Clojure etc). Find nominal interest rate given principal initial amount, future ...