Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [finance]

Questions related to the various aspects of financial mathematics. Topics include option pricing, arbitrage theory, market completeness and stochastic analysis.

Mathematical finance, also known as quantitative finance, deal with finance and financial markets in a mathematical manner.

Some examples of mathematical finance are the fundamental theorem of asset pricing which provides the conditions for a market to be arbitrage-free and complete, and the Black–Scholes equation, which uses partial differential equations to describe the price of an option over time.

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2637 questions
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Yield of 2 investments

For an initial investment of $1000$, investment A pays $100$ every year for $10$ years, starting from the end of year 1, plus a bonus maturity payout of $1000$ (i.e you receive a total of $1100$ at the end of the tenth year), while investment for…
Tosh
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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: let MP = 100 D=20% => SP = 80 SP = 80 P = 25% SP …
Ghost
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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, assume the S&P100 market index has performed like…
Pr0no
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Mathematic formula for increasing a number by a percentage every other time

I'm trying to create a formula where a number is increased by a certain percentage, then next calculation it is not, then the next calculation it is, then the next calculation it is not... Basically a pattern of increasing a number every other time…
C. Bildstein
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Present value of a perpetuity with continuous stream of cash flow

The present value of a perpetuity (cash flows paid at the end of each year) is $PV = CF / r$ where $r$ is the interest rate. This formula is proved in the book that I'm studying, Principles of Corporate Finance. However, then it is stated that if…
puk300
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implied volatility

I have a question about calculating the implied vol. Assuming the implied vol that a option will expire in 1 day is $\sigma_1$, and the implied vol that the option will expire in 2 days is $\sigma_2$. Is there a way to calculate the implied vol from…
Xiao
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Transpose Present Value of an Ordinary Annuity Formula for Interest Rate

I'm having trouble transposing the formula for Present Value of an Ordinary Annuity in order to find the interest rate. The formula is: Where P=Present Value of an Ordinary Annuity PMT=Payment i=Interest Rate n=Number of Terms Not sure if it…
BlueRhapsody
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Question on share valuation involving rate of return and dividend

BLC industries is expected to pay a dividend of $1.50$ and the dividend is expected to grow at a constant rate of $7$%. This stock is $15$% less risky than the market as a whole. The risk-free rate is $6$%, and the equity risk premium for the…
Tosh
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Nominal rate of interest for interest reinvested.

Sally lends $10000$ to Tim. Tim agrees to pay back the loan over $5$ years with monthly payments at the end of each month. Sally can reinvest the the monthly payments from Tim in a savings account paying interest at $6$% compounded monthly. The…
Tosh
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Re-investment of interest

Thomas invests X into Fund $1$ at the beginning of each year for $10$ years. Fund $1$ pays interest annually into Fund $2$. Fund $1$ earns $7$% annually while Fund $2$ earns $6$% annually. After $10$ years, Thomas has a total of $50000$. Calculate…
Tosh
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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: population in 1985 = 1,85,220 rate=5% time = 3yrs ( A=P(1-R/100)^n ) therefore, population in 1982 = 185220(1 -…
Nirvan
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Outstanding loan balance

A loan of ${$1000}$ is being repaid with annual payments over 10 years. The size of the payment in the first five years is ${$ k}$. It is found that the payments in the last five years are five times the payments in the first five years. Let the…
Tosh
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Loan to be repaid with the interest of the last payment given

A $60$-month loan is too be repaid with level payments of $1000$ at the end of each month. The interest in the last payment is $7.44$. Calculate the total interest paid over the life of the loan. Let effective interest be $j$. I tried finding the…
Tosh
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Calculating benefit of paying off loan ahead of time

So I'm doing a little financial planning, and I'm looking into the worthwhile-ness of paying off my student loans as quickly as possible. Being that I have multiple student loans, I combined them all together in a weighted average, putting me at…
yathern
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mortgage math problem

There's a $30$-year home loan for \$$100000$ at $7$%. After $15$ years the loan is paid off in order to refinance at a lower rate. The loan has a prepayment penalty of six months interest of $80$% of the remaining balance of the loan. a) How much is…
Matt
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