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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Ordinary Annuity Future Value Formula Explained

I am trying to conceptually understand the formula for the future value for an ordinary annuity. I do not want to just plug and chug, but rather to understand why the formula $$\text{FV }=\text{ pymt }\cdot \frac{(1+i)^n - 1}{i}$$ works the way it…
user732877
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1 answer

Calculating percentage reduction from results only.

I've been looking over some loan repayment statements, and I'm trying to work out: What the precentage interest is per month. How long it will be until the final amount reaches 0. Whether there is any modification to the percentage interest as…
Mere Development
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2
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2 answers

Solving for compound interest and annuities

Sandra’s grandmother set up an investment portfolio when she was 20. She invested $200 every year and earned an average annual interest rate of 8.8%, compounded annually. When she was 75 years old, she redeemed the investment and invested all the…
Savannah
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2
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2 answers

Solving bond duration

I am supposed to calculate the following problem: The Company issued 5,000 dollars voucher bonds with a half-year return of 100$ and a maturity of 8 years. Determine the duration of the bond if the normal annual yield of the probable bond is 6%. I…
Peter F.
  • 463
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Calculating the time before an investor makes profits on a cash flow

Question: One year ago an investor purchased a old house for £100,000 with the purpose of refurbishing it and then either letting or selling it. For the refurbishment the investor paid £50,000 one year ago for the materials. Until now (i.e. during…
Nipster
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2 answers

Finance: Breakeven Rate of Borrowing vs. Investing?

To calculate the $n$-period payment $A$ on a loan of size $P$ at an interest rate of $r$, the formula is: $A=\dfrac{Pr(1+r)^n}{(1+r)^n-1}$ Source: https://en.wikipedia.org/wiki/Amortization_calculator#The_formula And so the total amount paid over…
Drew
  • 415
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Compound Interest - Changing interest rates

Problem Calculations Hello, my problem involves compound interest specifically with changing interests. I tried doing the problem above by doing it in (2) and even tried putting it in a solver to do my calculations for me. Not fully sure the method…
IncognitoBatman
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2
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Mathematics of Finance changing rates and payments

Anyone can help with this question? I found out the amount that wouls have to be paid at the 7% interest rate and then subtracted it from the 25000 and worked out the new payment but its not correct(https://i.stack.imgur.com/gb8tJ.jpg)
Ocean Of Style
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Where is the error in my attempted derivation of the result $i^{(p)} = p[(1+i)^\frac{1}{p}-1]$?

Suppose $i^{(p)}$ denotes the nominal interest rate, payable as $\frac{i^{(p)}}{p}$, at a rate of $p$ times per period, and assume that $i$ is the effective interest rate (payable once per period) that is equivalent. Then, by considering the…
J. Chapman
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Hidden Markov model in Credit risk modeling

Could you please help me to understand what is a standard (multinomial) logistic link function between $X_{t}$ and the entries of $Q_{t}$ used in 'Modeling Portfolio Defaults using Hidden Markov Models with Covariates', which were written by Konrad…
Iwona Grabowska
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2
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2 answers

Compound interest ($r$ in terms of $\frac{dA}{dt}$)

Suppose the amount of money in bank account that is compounded annually is given by $A(t)$. The annual rate of interest is $r$. Find a relation between $\dfrac{dA}{dt}$ and $r$. My attempt: $$A(t)=A(0)(1+r)^t…
Siddhartha
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How to compare periodically and continuously compounding interest, when time is in-between periods?

I am working on a textbook problem, and I think I disagree with the solution. The problem is (10.6) Bruce deposits 100 into a bank account. His account is credited interest at a nominal rate of interest of 4% convertible semiannually. At the…
ajnelson.alpha
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Macaulay and Modified Durations

The current price of a bond having annual coupons is $1312$. The derivative of the price function of the bond with respect to the yield to maturity is -$7443.81$ when evaluated at the current annual yield, which is 7%. Calculate the Macaulay…
uytt
  • 75
2
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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 the year. Yet each month the total amount is…
caub
  • 267
2
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2 answers

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 Interest rate: 15% Number of payments:…
Minimul
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