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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Reinvestment calulators

I was wondering if someone can direct me to, or explain, calculations regarding reinvestment. For instance, say your initial investment is \$15,000, and via investing in stock you typically have a monthly return \$1,500 (10%), and you reinvest that…
Patrick
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Instalment APR Calculation Formula

I have a problem that I cannot solve regarding interest payments, and payment holidays. The scenario is this If I purchase a product which is paid for over a 12 month period, I need to calculate the monthly interest payments. However, the complexity…
Codemwnci
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1 answer

Sunk Costs NonRefundable Deposit

A young couple has made a nonrefundable deposit of the first month’s rent (equal to 1,000 dollars) on a 6-month apartment lease. The next day they find a different apartment that they like just as well, but its monthly rent is only 900 dollars.…
M.A
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2 answers

Calculating monthly reduction in value

If I can assume a value of $100,000 will reduce by a sum of say 25% each year, how do I calculate the amount it will reduce by each month over a period of 3 years.
Darren
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1 answer

Stochastic Finance I am having difficulty with my homework questions. Brownian Motion

A 2-dimensional process $(B_t^1,B_t^2),\ t \geq 0 $ is a standard 2-dimensional Brownian Motion if each $B_t$ is a standard Brownian motion and the $B_t^s$ are independent of each other. Let $ X_t = t^2 + \sin B_t^1 + B_t^1B_t^2$. Calculate $dX_t$,…
user146387
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1 answer

What is present value of the carbon expense for five years?

Suppose I have computed the cost of carbon per mile for my car at 0.009 per mile. Assume that the interest rate is 5% and that I drive the car 20,000 miles per year. What is present value of the carbon expense for five years? You will need to…
Darneezie
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I derived a formula for SIP calculations myself, but I'm unsure if it's accurate. Could you please help me verify it?

This is the formula I derived Here, for simplicity, P is the amount you invest every year, T is the total number of years you invest your money, and R is the Interest Rate for every year. Please someone verify this formula and suggest some…
Koro
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1 answer

What is the formula for the ratio of the principal payment and interest payment for a loan, given a fixed interest rate and loan term?

I just saw a youtube video where they mentioned that a closed-form solution exists, bypassing the need for an amortization table. This was framed in the context of having multiple loans to service and just wanting that ratio. They said they wouldn't…
Adrian Fletcher
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1 answer

Financial Calculation with compound interest: Determine how much a person will need to have saved in year 0 of retirement based on monthly withdrawals

I am trying to come up with a formula to determine how much a person will need in retirement. So every year, they will take their inflation-adjusted withdrawals out of their retirement savings, and the remainder of their savings will accrue a return…
rook218
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1 answer

How to convert continuous interest compounding rate to non-compounding rate?

Let's say we are told that a bank offers an annual interest yield of 50%, and it is automatically compounded by the bank. Assume the compounding is done continuously rather than in discreet intervals. How can we calculate what the yield would be…
David Callanan
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1 answer

Deriving APY from starting and ending balance

Suppose I have a starting balance of 3000 USD and at the end of the month I have a final balance of 3600 USD. How would I calculate what the APY is based on just the starting and ending balance?
EcomEvo
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1 answer

Compound Interest problem , loan amount

A lent £80,000 to B with the assurance that B would return £50,000 every year for two years. What is the approximate rate of compound interest per annum that A is charging B? (A) 11.8 % (B) 25 % (C) 18.75 % (D) 16.25 % My approach:- My approach is…
Fin27
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Find the loan amount borrowed

I am working on the EMI calculator module as part of the current banking project. I find answers for calculating simple interest, EMI, and even tenure but not able to find a formula to calculate the total amount borrowed. I found the below formula…
anonymous
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1 answer

Finance Question (involving interest that is added)

I have 2 questions involving this concept, that I am looking for an answer for. Tony is considering putting 50 dollars per month into a special account that would earn 6.25% annual interest. How much would Tony have in his account after 25 years?…
gocowboys
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What could the formula of the present value for such a saving plan?

Trying to make the problem as simple as possible. I decide to start on January $1^{\text{st}}$ a saving plan for which the bank will give me a constant interest rate $r$ (the interests being paid on December $31^{\text{st}}$). During a given year…
Claude Leibovici
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