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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2
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1answer
35 views

How to calculate savings over the life of a car loan?

I'm working through the maths in this, only the relevant parts of which I quote: ...On a \$25,000 car loan through the manufacturer for four years, your monthly payment would be about [1.] \$520 ...
2
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0answers
54 views

Simplifying $\sum_{t=1}^{n}t^2v^t$ using actuarial notation.

In financial mathematics involving immunization, I encounter situations where I am trying to calculate $$(A) \quad v+4v^2+9v^3+ \cdots +n^2v^n=\sum_{t=1}^{n}t^2v^t $$ where $v$ is the present value ...
2
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0answers
29 views

Are these two option valuation formulas equivalent? Why?

I have been reading a finance paper that claims that the following function, which is a value for a financial derivative (1): $$V(s,t)=E_{Q} \left[\zeta\big(S(T)\big)e^{-\int_t^T r_F(\nu) ...
2
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0answers
25 views

Macaulay duration for a coupon bond. Proof

I am working on showing the following. There is a coupon bond redeemable at par with annual coupon rate $r$ per year. The yield to maturity is $i$. The total number of coupons is $n$. Show ...
2
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0answers
32 views

What is this sort of optimisation called?

I am reading a book in mathematical finance. There is something about constrained optimisation. They have specialised it for the financial market, but I am wondering what the general name for this ...
2
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0answers
36 views

Pricing/Valuation of American Options

Hi i'm a litte bit confused by the pricing valuation of American options. For simple Assumtions on the Blacksholes Model and no dividends, and constant rates else one can show, that for a given ...
2
votes
1answer
20 views

Total MSRP given monthly payment, downpayment %, and term of autoloan

I want to buy a car. I know the following: - monthly payment - interest rate - # of months of loan - downpayment % How can I calculate the total MSRP I can get for my monthly payment? So for ...
2
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0answers
14 views

How to calculate present value with changes interest

How to calculate present value with period of 5 years and 6 months? Besides that, there is interest changes and compounded differently. Is there any formula?
2
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1answer
38 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
2answers
75 views

Are there other accumulation functions that holds $a(n-t)={a(n) \over a(t)}$?

This might be a beginner's question regarding accumulation methods and their functions, but so far I have learned that compound interest satisfy $$a(n-t)={a(n) \over a(t)}$$ Which allows nice ...
2
votes
1answer
30 views

Saving for retirement - how much?

I'm working through a problem in the book "An Undergraduate Introduction to Financial Mathematics" and there is an example I can follow. The problem is: Suppose you want to save for retirement. The ...
2
votes
1answer
39 views

Understanding APR - can it be calculated as a dollar amount

If the APR (as used in the US Truth in Lending Act) is considered "the cost of your credit as a yearly rate," can an APR be converted to a dollar amount? For example 10% simple interest per year on a ...
2
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1answer
29 views

the relationship between fractional difference and ACF of a time sequence

When reading the GARCH modeling part of book Analysis of Financial Time Series, I read the following statement. In specific, I do not understand how does the author ...
2
votes
2answers
100 views

Understanding basic stochastic differential equations

This is from a physics course in economics, the literature provides a bare minimum of mathematical explanations. I am trying to understand how to work with stochastic differential equations given in ...
2
votes
1answer
30 views

Find APR with loan balance

Here is the problem: L: original loan amount B: current balance after P periods P: number of periods that have been paid A: period payment **you do not know the number of periods remaining, so ...
2
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0answers
129 views

Engineering Economics Cash Flow Diagram

I have the following question and solution below. What I don't understand is why is the 100,000 seen as savings/revenue when clearly it is coming out of pocket? Additionally, the monthly loan payment ...
2
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0answers
155 views

What does it mean to “pass to the limit” in mathematics?

I've been reading a finance paper and stumbled upon this phrase. What does passing to the limit mean in this context (or overall in mathematics)? Here is an excerpt from the paper: It is ...
2
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0answers
44 views

Reinvesting the interest (generalized version)

If I deposit \$1 at $t=0$ into an account which credits interest at the end of each year at a force of interest $\delta_t$ (assume it's integrable.) Then, if I reinvest the interest at an annual ...
2
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2answers
57 views

quartely payment

A Loan of R65 000 with an interest rate of 16% per annum compounded quartely is to be amortised by equal quartely payments over 3 years Question : how do I calculate the size of the quartely payment? ...
2
votes
1answer
78 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
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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 ...
2
votes
1answer
53 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 ...
2
votes
0answers
85 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 ...
2
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0answers
28 views

Standard practice for identifying outlying spend amounts

Hope this is mathematical enough to qualify as a question - I'm no mathematician! I have a set of individuals travel & entertainment credit card spend, and I'd like to highlight any outliers that ...
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vote
4answers
2k views

Second Price Auction (Generalized Second Price)

I am trying to find out why we pay second price, but can not understand it. All that I found it is an explanation that it is a real market price, but why it is ? May be some example helps me. For ...
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3answers
196 views

Paying Debt Off in a year

I want to know how to calculate minimum fixed monthly payment needed in order to pay off a credit card balance within 12 months. I just want to understand the concept, and how to work around this ...
1
vote
2answers
510 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? ...
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vote
2answers
89 views

Why can moving averages of the prices indicate the trend of a stock?

In technical analysis of stock trading, we can use the moving averages of the historical prices of a stock to indicate whether it is currently in the uptrend or downtrend. Let me exemplify the idea ...
1
vote
1answer
464 views

today's price of a European put option with payoff $(K-S_1)^+$

I'm trying to calculate the today's price of a European put option, which strikes at price $K$, so that the payoff is $(K-S_1)^+$, in an arbitrage-free, one-period market. As of now, I can only think ...
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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, ...
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2answers
173 views

how seconds per year does the average worker work?

Approximately how many seconds per year does the average 18 – 21 year women factory worker work? Choices are... A] 2,526 B] 80208 C] 5700 D] 3,443 E] 3958 assuming Accident per person per year is ...
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2answers
46 views

What is a discount?

I am learning some financial terms and am having trouble understanding what a discount $d$ is. Numerically, I understand that it is defined as $\frac{i}{1+i}$ but I do not intuitively understand what ...
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2answers
163 views

Solving i for annuities equation without financial calculator

I would like to know if there was a way to approximate i here without a financial calculator, in the following equation: $\displaystyle -50000 + \frac{12992}{1+i} + \frac{12992}{(1+i)^2} + ⋯ + ...
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4answers
6k views

No-Arbitrage Principle

I hope you do not mind me asking a financial question in this section. I am having trouble understanding the concept of the no-arbitrage principle for a particular example in my notes: Suppose a ...
1
vote
1answer
193 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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2answers
34 views

Calculating monthly compounded interest

To solve the problem How long does it take for an investment to double in value if it is invested at 8% compounded monthly? I figured like this: $$2P = P(1 + 0.08)^t$$ where $P$ is an ...
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2answers
47 views

Amortize the debt problem

Monthly payments are made on 130000 dollars at 5% for 25 days. Determine the payment needed to amortize the debt.
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2answers
145 views

Find prize per unit that will maximize profit at a given $x$-value

Struggling while reviewing my old math books. The problem has a prize-function and wants to know how the prize-per-unit should be chosen to maximize the profit at $\mathbf{x=160}$. First I look ...
1
vote
1answer
52 views

How do i solve this to find PMT?

I know this may seem like a stupid question but i've been up late working on this math assignment and this question just isn't working when i transpose it. So this is the formula to find Present ...
1
vote
1answer
15 views

Finding the compounding period

The future value of a 200 deposit in an account that earns 6.25% annual interest is $272.71 after 5 years. Determine the compounding period for this investment. This is what I have done: $272.71= ...
1
vote
1answer
952 views

Black-Scholes PDE to heat equation, nonconstant coefficients

Can someone provide me with details or a reference on how to transform the Black-Scholes PDE with nonconstant coefficients (i.e. $r=r\left(S,t\right)$, $\sigma=\sigma\left(S,t\right)$) to the heat ...
1
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3answers
102 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})}{ ...
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3answers
11k 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' ...
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2answers
224 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 $4^{\rm th}$ ...
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2answers
304 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 ...
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2answers
113 views

How to solve for $i$ and $n$ in compound interest formula?

Given that $$F = A{ (1+i)^n - 1 \over i}$$ How can you solve for $i$ or $n$?
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1answer
191 views

How to compute ideal investment leverage ratio based upon volatility? [closed]

I want to compute the ideal investment leverage ratio based upon an investment's volatility. For example, if I had an investment that with 50% likelihood quadruples your investment on a given day ...
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vote
1answer
7k views

How do you calculate “excess returns”?

(Although this is perhaps a very simple question, math-wise, it still has me puzzled so it's okay to ask for help here I guess. I really need to understand this, so any help is appreciated) First, ...
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2answers
26k views

Calculate gross salary when knowing the net salary and tax brackets

Assume the annually gross salary is $100,000. Tax brackets: 0 - 50K - 10% = 5K in taxes 50K - 70K - 20% = 4K in taxes 70K - $90K - 30% = 6K in taxes 90K and up - 40% = 4K in taxes The income tax ...
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2answers
109 views

Calculate breakeven when fixed revenue being added per month v/s cost

I am writing up a cost sheet for a product and I basically suck at math. Didn't know who else to turn to, so trying out Math exchange. So, I am planning to spend ...