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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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 years. He wants to collect $1,000,000 by…
user3472798
  • 507
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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 2.32%, in order to fund the scholarship? This…
user3472798
  • 507
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Proving implications of equations

I'm currently working on the finance problem: If we define $I_k$ = A(k)-A(k-1) then $\sum_{k=1}^n I_k$ = A(n) - A(0) show that this implies $\sum_{k=1}^n i_ka(k-1)$ = a(k)-1 So I know that our top equation is a telescoping sum, and every value will…
user3472798
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What is the Future Value of a $\$5{,}000$ loan paid back at $\$1{,}000$ per month, with a $6\%$ nominal interest rate?

I'm trying to figure out a problem with the formulae I have, but I'm having some difficulty. The problem is: Susan borrows $5{,}000$ dollars from a finance company at a nominal interest rate of $6.6\%$ compounded monthly. If she makes payments of…
user3472798
  • 507
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Mathematics of portfolio rebaance

I would suspect that a financial maths book would introduce the following, but I am only a novice and so would cherish your recommendations. The following is motivated by pp 304-305, ETFs for Canadians for Dummies (2013; by Russell Wild and Bryan…
user53259
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What equal installment of annual payment will discharge a debt which is due as 848 at the end of 4 years at 4% per annum simple interest?

What equal installment of annual payment will discharge a debt which is due as Rs. 848 at the end of 4 years at 4% per annum simple interest? The above question can be calculated by using the formula $$x= \frac{100P}{100n+\frac{n(n−1)r}{2}}$$…
kodewhiz
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Bank interest but reversed problem - how much was the first money deposited?

Suppose I have money ($x$) in a bank account bank with compound interest of $5\%$ annually paid monthly. Bank gives me $20,000$ usd a month and the money $x$ finishes in $20$ years ($240$ months). How to calculate how much was $x$? For example if…
user200918
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I have just signed a lease

I have just signed a lease that requires me to repay $\$100,000$ over $10$ years with payments starting today. What is my annual repayment if the effective interest rate is $7\%$ per annum? I did (100000)/(1-(1/(1+0.07^10))/0.07 * 1.07 which…
Jackie Ao
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How to calculate interest rate given cash flows and period in days instead of years.

I am presented with an investment opportunity where I am given #481,000 on day 1. Thereafter, every 10 days, I am required to give back #50,000 every for 100 days (10 * 50000 = 500000). How do I calculate the interest rate I am paying? I am guessing…
newbie
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Strange Monte Carlo Sampling Phenomena

I am running a Monte Carlo simulation to price call and put options, and observe a strange correlation between the number of sampling points and the standard deviation. It makes sense that as the number of sampling points approaches infinity that…
Kerry
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Lower semicontinuous risk measure

I am looking for some risk measures that hold the lower semi-continuous property. I am not sure whether Expected Shortfall is a such a measure or not. Can anyone give me some help？ Thanks.
ndor
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Calculate interest over multiple years with added value every year?

I'm trying to calculate the interest and total of money when : Someone is loaning $3600 every year over 11 years with an interest of 10% ? Like : 3600 + 10% = 3960 first year, 3960+3600+10% = 8316 second year etc. Just that I need a formula to…
wamp
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Semi Annual Deposit Compounded Quarterly

A son planned to endow 1000000 to his son on his son's 21st birtthday. How much is his semi-annual deposit in a special account that earns 5% compounded quarterly if the first deposit was made when the son was 4.5 years old? The answer is 16640.20 I…
james
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Compounded Quarterly

Money borrowed today is to be paid in 6 equal payments at the end of 6 quarters. If the interest is 12% Compounded Quarterly. How much was initially borrowed if quarterly payment is $2000 Answer is $10834.38 I've tried the Compound Interest…
james
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Money doubling in value

I understand this maybe a question for https://quant.stackexchange.com/; but I believe the math is simple enough to understand. In How many months at an interest rate of 1% per month does money have to be invested before it will double its…
james
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