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
48 views

Force of interest :$e^{\int_0^t{\delta_t}ds}$ vs $(1+\frac{i^{(2)}}{2})^2$

I was wondering if someone could help me confirm the answer for the following problem regarding force of interest. X deposits $1$ at time $t=0$ with force of interest $\delta_t=\frac{t^2}{k}$. Y ...
0
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1answer
125 views

182-Day T-Bill vs. 91-Day T-Bill

I am trying to understand how T-Bills work and it would be great if someone could explain me using the following question At $t=0$ Smith buys a 182-Day T-Bill with a simple annual discount rate of ...
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1answer
30 views

“Cost per Lead Quality” Score

I'm a marketing manager and would like to calculate a cost per lead quality "score." I run a number of marketing campaigns, and I've figured out how to calculate a quality percentage for each campaign ...
0
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1answer
947 views

Discount rates vs. Interest rate problem.

I am working on a problem as follows. A discounted value $X$ that is due when $t=0.5$ has a present value \$4992. Calculate the value of $X$ when a), the effective annual compound interest rate ...
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1answer
61 views

Finance problem - Canadian bond with simple interest

I am having trouble understanding a lot of things from the following problem. It would be very helpful if I could get some explanations. Smith purchases a Canadian bond for 1000 with an issue ...
0
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1answer
23 views

Problem regarding Investments and selling the right.

I have trouble solving the following problem algebraically. Smith lends $\$1000$ to Jones at time $t=0$. Jones is supposed to repay Smith by paying $\$100$ at time $t=1$ and $2$, and $\$1000$ at ...
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2answers
37 views

Proof $(1+i)^t < 1+it$ if $0 < t < 1$

I am trying to prove that compound interests grow slower than simple interest in the first year. I attempted to do this with the following approach. Let $$f(t) = (1+i)^t$$ then $$f'(t) = ...
0
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1answer
27 views

Future value of investment with quarter payment

I'm a bit stuck on this problem, tried to solve it, but I don't know what is wrong with my way of thinking. A bank offers a deposit with the interest rate of 5% per annum with quarterly interest ...
1
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1answer
112 views

The meaning of “average annual compound rate”

I am currently working on this problem and I am having a hard time finding the right number. A mutual fund advertises that average annual compound rate of returns for various periods ending Dec 31 ...
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0answers
40 views

Finding the annual withdrawal, given initial and final amounts, and interest rate

I am working on the following problem and I keep getting a different answer. The principal $P=10,000$. The annual interest rate is $i=4\%$. The money is deposited at time 0 and the interest is ...
0
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1answer
31 views

Find the balance using Investment Year Method…

Here's the problem: Now, here is what I did: Since we invested $\mathbb{$}1000$ at the beginning of $1989,1990$, and $1991$, we find the balance of each contribution over the specified ...
2
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2answers
87 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
2answers
270 views

Deriving Black Scholes using CAPM

I am referring to http://www.frouah.com/finance%20notes/Black%20Scholes%20PDE.pdf Section 3, which is a bit more detailed version of the original derivation from ...
1
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1answer
114 views

Calculate repayments amount on loan

I doing some work on a client website, however I'm finding it difficult to calculate the correct interest amount. I have the principle amount, for example £200 The loan is repaid over 3 months in ...
0
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1answer
128 views

Derivation of Efficient Frontier (portfolio optimization) question

In Robert Merton's derivation of the efficient frontier of a portfolio, he minimizes $\frac{1}{2}\sigma^2 $ over the investment weights in each asset, where $\sigma^2$ represents portfolio variance. ...
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1answer
66 views

Put-Call Parity

This question is from Pliska's "Introduction to Mathematical Finance" Suppose the interest rate r is a scalar, and let c and p denote the prices of a call and put, respectively, both having the same ...
1
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2answers
61 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 ...
0
votes
1answer
124 views

How to calculate total loan knowing only the APR, term and monthly payments?

I'm building a loan calculator with two different methods of user entry. One one side the user can enter their desired loan amount and specify a term and it will display the overall loan amount and ...
0
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1answer
25 views

Help on understanding tax bracket computation

Warning: some codes Tax Bracket: 1 up to 5,070 ---- 10% ...
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2answers
72 views

Present Value (Interest)

The question goes like this: What deposit made today will provide for a payment of 1000 in 1 year and 2,000 in 3 years, if the effective rate of interest is 7.5%? The answer given by the book is ...
2
votes
1answer
34 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 ...
1
vote
1answer
200 views

Recursive Solution to Interest with Monthly Deposits

I open an account at a bank with 1% interest compounded monthly. I'm adding $100 to it at the beginning of each month (starting with month 1). (a) Set up a recurrence relation for the amount in the ...
1
vote
1answer
89 views

Problem regarding equation of value and nominal discount…

Here's the full problem: Xiang and Dmitry are friends. They agree that Xiang will pay Dmitry $\mathbb{$}800$ immediately and another $\mathbb{$}200$ at the end of three years. In return, Dmitry ...
0
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1answer
121 views

Problem involving nnual dollar-weighted yield-rate on stocks…

Full problem: Arthur buys $\mathbb{$}2000$ worth of stock. Six months later, the value of the stock has risen to $\mathbb{$}2200$ and Arthur buys another $\mathbb{$}1000$ worth of stock. After ...
0
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1answer
130 views

Guess-and-check for annual effective interest rate and annual yield rate

Here is the full problem: Kurt loans Randy $\mathbb{$}14000$. Randy repays the loan by paying Kurt $\mathbb{$}4000$ at the end of one year and $\mathbb{$}6000$ at the end of two years and as well ...
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0answers
30 views

Does interest apply for the last month of an amortization?

I'm working out the loan repayments using the amortization formula $$\frac{\text{principal} \cdot \text{paymentPercentageInDecimal}}{1 - (1 + \text{paymentPercentageInDecimal})^{-\text{payments}}}$$ ...
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2answers
72 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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1answer
72 views

Solving Black scholes PDE using Laplace transform

I'm trying to obtain the Laplace transform of Call option price with repect to time to maturity under the CEV process. The well known Black scholes PDE is given by $$ ...
1
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1answer
36 views

Prove $\sigma_V=x\sigma_S$. (Financial Mathematics)

Prove that the standard deviation of the value $V(T)$ at time of any portfolio $(x,y)$ at time $T$ in a one-step binomial is given by $\sigma_V=x\sigma_S$, where $\sigma_S$ is the standard deviation ...
0
votes
1answer
34 views

Is there a way to do this? Fixed deduction for x rounds where total = fixed amount

I am trying to calculate the reduction amount / step per round for the given: rounds = 1000 points = 80 starting at reward = 1 point So from round 1 which has a reward of 1 point deduct a fixed ...
1
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1answer
81 views

Markov property question

In every book I can find, the Markov property for ito diffusions, $E[f(X_{t+h})\mid F_s] = E^{X_t}f(X_h)$ is stated for $\textbf{bounded}$ Borel functions. However, I have the following statement ...
1
vote
1answer
29 views

Compound interest problem with increasing deposits

An Investor starts with an initial investment : $A$ He earns a steady profit of 10 percent per year. But every year he adds additional amount which increases by 15 percent every year. At the end of ...
0
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0answers
64 views

Reverse Engineer Math(financial) Answer.

I'm starting to question the Payment amount generated by the software my lender is using, but it could be my calculations that are wrong. I would like confirmation before I proceed. Is my approach ...
1
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0answers
66 views

Locate proof of Second Fundamental Theorem of Asset Pricing

Where can I find a $\textbf{rigorous}$ proof of the Second Fundamental Theorem of Asset Pricing. That is, A market is complete if and only if it has a unique risk neutral measure. Please do not ...
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
votes
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 ...
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2answers
219 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
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1answer
278 views

Effective interest rate given two loan payment options…

Here's the full problem: You have two options to repay a loan. You can repay $\mathbb{$}6000$ now and $\mathbb{$}5940$ in one year, or you can repay $\mathbb{$}12000$ in $6$ months. Find the ...
1
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0answers
62 views

Intuition behind American option pricing

The price of an American option is given by $V_n = \max\{G_n, \frac{1}{1 + r}(pV_{n +1}(H) + qV_{n + 1}(T)\}$, where $p$, $q$ are the risk neutral probabilities. I have two questions. How can ...
2
votes
1answer
98 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 ...
1
vote
1answer
58 views

My doubt about a problem of financial mathematics.

I state that I am italian, so, if there are some mistake in my questions say it to me, and I correct as soon as possible. I've known this forum in an italian forum about molecular biology, where I was ...
1
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1answer
78 views

ROI Forumla for this scenario

I couldn't come up with a proper formula for the scenario below. I'm not so good at Maths. With, $X$ - monthly gains in percentage $C$ - Initial capital $N$ - number of years $M$ - Amount ...
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2answers
57 views

Pay back loan with an annual withdraw

I was given question 7b as homework: I am guessing that there are numerous ways of approaching this. The one method I have tried was to calculate the effective interest year for the year. Then ...
1
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1answer
143 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
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2answers
58 views

Bactracking to find compound interest

I'm trying to find what percentage 5000 dollars compounding monthly over 120 months will be if the final sum will be 7000 dollars. So: 7000=5000(1+r/12)^120 When working backwards to find r I ...
6
votes
2answers
583 views

Proof of the Black - Scholes pricing formula for European Call Option

I want to prove the following The price of a European call option with strike price $K$ and time of maturity $T$ is given by the formula $\Pi(t) = F(t,S(t))$, where $$F(t,s) = ...
2
votes
2answers
64 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) ...
0
votes
1answer
192 views

Derivation of Black-Scholes equation by riskless portfolio

The following is a summary of the derivation of the Black-Scholes equation as given on wikipedia (http://en.wikipedia.org/wiki/Black-Scholes_equation#Derivation) - I have a question regarding the ...
0
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1answer
27 views

Formula for fitting step-wise increasing loan payments into a given term

My company is developing a product that helps people project out what-if scenarios for paying down their student loan debt. One of the government options for paying off debt is called the "graduated" ...
1
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2answers
73 views

How much more than will you pay on a 30 year mortgage than if you paid it all up front?

There are hundreds of loan calculators online but none of them tell me this, Say I take out a 30 year mortgage on a 80,000 dollar house for 4% interest. How much more than $80k will I spend at the ...