Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

learn more… | top users | synonyms

1
vote
2answers
290 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 ...
2
votes
1answer
3k views

How to convert interest rate to discount factor

I'm studying on Kellison's Theory of Interest and I'm stuck on the exercise 20/a of the 1st chapter. If the $i=0.1$ then $d = 0.0901$ $d_5=\frac{A_5-A_4}{A_5}$ when I insert $d$ into this ...
0
votes
1answer
130 views

Trouble arranging for interest in annuity to present value formula

The formula is: $$A = P\frac{i(i+1)^{n}}{(i + 1)^{n}- 1}$$ and I need to rearrange for $i$ because I don't know the interest. I can solve this if it were Any help would be greatly appreciated.
1
vote
2answers
69 views

Value of Investment in the Past

An amount of $1000$ is to be accumulated at a compound rate of discount of $9$% per year. (a) Find the present value $3$ years before (b) Find the value of i corresponding to d. For a) i have done ...
0
votes
2answers
424 views

Determine the simple interest rate under which a sum of money will double in 5 years.

Determine the simple interest rate under which a sum of money will double in 5 years. IS my following solution correct below? $A = p(1+r)^{t}$ $A/p = 2 =(1+r)^{5}$ $ln2 = 5ln(1+r)$ $ln2/5 = ...
2
votes
2answers
66 views

Cost for hedges under a Wiener process

I'm trying to estimate the hedging costs relating to a financial derivative which moves like a Wiener process, and I'm struggling to find the correct setup to solve the problem. Suppose I have a ...
0
votes
1answer
70 views

European Calls: arbitrage

I have following question, it should be pretty easy, but this subject is still pretty new for me. Given a market where calls of any strike price can be bought and sold. Assume that the interest rate ...
1
vote
1answer
4k 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 ...
0
votes
2answers
113 views

Calculating deposit based on interest and required withdrawal in future

I am really stuck with example 2-5 and 2-6. I don't really understand example 2-6 and example 2-5 I just can't figure out...I was able to do example 2-4 which was easy... For example 2-4 I did F=P(1+ ...
1
vote
1answer
91 views

Isolate a variable in this financial formula

I'm trying to build a programming function that returns the value o CET so I need to isolate it. How can I isolate CET so I get something that can I linearly solve using a programming language? ...
2
votes
2answers
63 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 ...
0
votes
1answer
587 views

Early withdrawal fee for compound interest CD investment

Suppose you buy a CD for $1000 that earns 2.5% APR and is compounded quarterly. The CD matures in 5 years. Assume that if funds are withdrawn before the CD matures, the early withdrawal fee is 3 ...
1
vote
1answer
907 views

Subtract simple interest from compound interest

Here's a question on compound interest and simple interest. The difference in compound interest and simple interest for 2 years on a sum of money is \$160. If the simple interest for 2 years be ...
3
votes
2answers
457 views

Independent math learning

I'm an undergraduate math and econ major and I'm planning on graduating relatively soon and I am very limited to the number of math classes I have left (very sad about this fact). So far I have ...
0
votes
1answer
79 views

Find the total percentage loss over a specified time frame.

If you had an investment and you consistently lost 5% of it per year for 6 years, how do you find the total percentage loss, without knowing the original investment?
1
vote
1answer
435 views

Finding a fix amount payment to payoff multiple credit cards in 24 months

Mr.Debt has 3 credit cards. First card have \$5,000 balance with the rate of 10% compounded monthly. Second card have \$2,000 balance with the rate of 14% compounded monthly. Third card have \$4,000 ...
1
vote
0answers
61 views

Interest % and final payment

I dont get these two questions? How should I calculate the answer? A) Sam intends to retire in 6 yrs. To supplement his pension he would like to receive $\$234$ every 2 weeks for 10 yrs. If he is ...
2
votes
1answer
175 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
votes
1answer
137 views

Black scholes model type

I want to study the following market: $$S_1(t)=S_1(t)(\mu_1dt + \sigma_1dW_1(t))$$ $$S_2(t)=S_2(t)(\mu_2dt+\sigma_2dW_2(t))$$ for $t\in [0,T]$, constants $\mu_i,\sigma_i$, initial values ...
1
vote
1answer
227 views

Compound interest quarterly

I know the financial formula for calculating compound interest: Compound Interest Multiple = [1+(Annual Interest in decimals/365)]^(number of days). I have a initial and final date. I calculate the ...
2
votes
2answers
593 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 ...
0
votes
1answer
29 views

Capping part of a sum

I have a financial constraint which states that: spend on x cannot exceed 15% of total spend, where ...
1
vote
0answers
344 views

Analogue of Leibniz Rule for Stochastic Integrals

Suppose $$f(t,u)=f(0,u)+\int_0^t{\mu (w,u)dw}+\int_0^t{\sigma(w,u)dB_w}$$, where $B_w$ is a standard Brownian motion. I would like to calculus the drift and diffusion of $Y_t=-\int_t^s{f(t,u)du}$ ...
1
vote
1answer
173 views

Net Present Worth Calculation (Economic Equivalence)

I'm currently doing some work involving net present worth analyses, and I'm really struggling with calculations that involve interest and inflation, such as the question below. I feel that if anyone ...
7
votes
2answers
276 views

Significant digits

We use currency conversion rates for financial calculations. Our currency conversion table stores conversion rates to and from each currency (about 150 world currencies) for each day, going back 20 ...
1
vote
1answer
98 views

PayDay loan APR

I'm not convinced I'm getting the correct figure when I calculate an APR rate. I have an amount I want to loan £100 I want to pay this back in 14 days. Interest for this loan is 15% The fee for this ...
0
votes
1answer
69 views

annuities and interest

The loan of 30.000 euros is depriciated after 10 years, with equal annuities and interest of 11% of annual capitalization. how can the annuity be determined? -this one seems to be the toughest of them ...
1
vote
2answers
38 views

Percentage of capitalization

After how many years the deposited sum of K-euros will triple itself if the interest percentage of capitalization is 12%, the capitalization is annual.
1
vote
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 $n$?
2
votes
1answer
586 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 ...
1
vote
4answers
1k 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 ...
1
vote
1answer
186 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 ...
1
vote
0answers
95 views

Uniform convergence of series with utility function

Let $u(x)$ be a real function with the properties $u(x)$ is continuous and non-decreasing in $x$ $u'(x)$ is non-increasing in $x$ $u(0)=0$ $u'(0)=1$. In other words, $u(x)$ is a utility function. ...
0
votes
1answer
91 views

Showing an inequality with interest rates and compounding

Suppose that your grandmother is receiving Social Security at the start of next year and has to choose between two plans for how to receive her payments. Divide each year into $k$ payment periods ($k$ ...
3
votes
1answer
2k views

Confused about Effective Rate of Discount- Theory of Interest

I'm currently reading Kellison's book, The Theory of Interest. I've reached the chapter on Effective Rate of Discount and it's somewhat confusing. The book explains it as a loan where interest is paid ...
1
vote
1answer
492 views

Help understanding confusing present value question (Theory of Interest)

I'm currently enrolled in a theory of interest class that covers the same material that's on exam 2/FM. At the instructors recommendation, I'm working through all of the problems in the book on my own ...
2
votes
1answer
386 views

How to get Annualized volatility from monthly return?

Suppose the average monthly return is $\mu$, the monthly standard deviation is $\sigma$ and denote the autocorrelation of monthly returns by $corr(r_i,r_{i+h}) = \rho(h)$ Prove that, when $\sigma$ ...
1
vote
1answer
541 views

How to find Profit percent in this case?

A trader allows a discount of 20% on his goods and still makes a profit of 25%.Find the profit percent made, if he sells his goods at: (1) the Marker price (2) at 10% discount What i've tried: ...
1
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, ...
1
vote
2answers
163 views

How to find the original population if it increases with a constant rate?

The population increases by 5% every year. What was the population in 1982, if in 1985 it was 1,85220? My working: ...
0
votes
2answers
2k views

How to find rate of depreciation in this problem?

The value of a machine is estimated to be 27,000 at the end of 1994 and 21,870 at the beginning of 1997. Supposing it depreciates at a constant rate per year of it's value at the beginning of the ...
0
votes
2answers
21k views

What is the formula for the difference between CI and SI?

if principal, time and rate are given how do i find the difference between Compound interest and Simple Interest? P=12,000 n=1 and a 1/2 yrs. R=10% per year ...
1
vote
1answer
134 views

Calculate Compounding Interest Rate From Total Interest Rate?

I would like to be able to calculate the interest rate that is compounded for a given total interest rate, and number of compounding events. TotalInterestRate = ...
3
votes
1answer
81 views

How the banker limits his risk?

In a game like Deal or no Deal, what is the formula the banker uses to give an offer to the contestant? The banker offers the contestant an amount of money to quit the game, the offer based roughly on ...
1
vote
0answers
100 views

Compactness of the set of densities of equivalent martingale measures

Consider an incomplete market $(\Omega,\mathcal F,\mathbb P)$ driven by a semimartingale $S=(S_t)_{t\in[0,T]}$. Under the no free lunch under vanishing risk (NFLVR) assumption, the set $\mathcal ...
0
votes
1answer
356 views

How to handle the following percentage scenarios?

I have the following scenarios, but I am unclear on how to handle them correctly. I start off with a value like 200 and the following scenarios are: Remove 10% from 200, and then remove a compound ...
1
vote
1answer
502 views

Formula for APR with Odd Days

I need to programmatically calculate APR based on the following inputs: Principal Amount Number of payments (for example, 3 months loan is 3 if paying monthly, or 6 bi-weekly payments) Payment each ...
1
vote
0answers
85 views

Good reference on sample autocorrelation?

I'm not a statistician but I'm writing my thesis on mathematical finance and I think it would be neat to have a short section about independence of stock returns. I need to get better understanding ...
1
vote
1answer
127 views

Book or resources to learn about algorithms for detecting arbitrage opportunities in slow markets (not HFT)

All of the trading algorithms I see online relate to high-frequency trading in fast-moving high-volume markets. Can someone point me to some resources about automated trading (detecting arbitrage ...
3
votes
1answer
255 views

Futures pricing and futures price process under the real world measure

This is something that keeps bothering me about the Benchmark approach of Platen, which (very) shortly is as follows: Compare the development of an economic value with a growth optimal portfolio. ...