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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find the amount of loan, principal and the interest.

A borrower is repaying a loan at 5% effective with payments at the end of each year for 12 years, such that the payment at the end of the first year is 220, at the end of the second year is 210 and so forth until the payment at the end of the12th…
user125984
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Find APR with loan balance

Here is the problem: L: original loan amount B: current balance after P periods P: number of periods that have been paid A: period payment **you do not know the number of periods remaining, so you do not know N (the total number of periods for the…
user129306
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Help me optimize my work

I am a physician. I am required to work 14 shifts per month. I may work extra shifts for 1400 dollars per shift. In addition, I earn productivity based on a system called RVUs. For every RVU I produce over 4100 for the year, I will earn an…
Docinabox
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Working out the difference in earnings

I'm mathematically impaired/ignorant and trying to figure out the difference in earnings between my partner and I to work out a fair split of the bills. So; I earn £2060 per month and partner earns £1650. As a percentage, how much more than her do I…
Matt
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2 answers

Bonds and Yield Rate

I came across the following problem on bonds: Suppose we are given the following term structure of annual effective yield rates for zero coupon bonds: $(1, 2 \%)$, $(2, 6 \%)$, $(3, 7 \%)$, and $(4, 7 \%)$ where the ordered pairs are of the form…
Damien
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Actuarial Science FM Question

$$a(t)=Zt^2+Bt+1$$ If \$100 at $t=0$ grows to \$152 at $t=4$ and \$200 at $t=0$ grows to \$240 at $t=2$, what are $Z$ and $B$? Please show work. Also, what would \$1600 invested at $t=6$ grow to at $t=8$?
steven
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quartely payment

A Loan of R65 000 with an interest rate of 16% per annum compounded quartely is to be amortised by equal quartely payments over 3 years Question : how do I calculate the size of the quartely payment? Will I = 0,016/4 and will n =36 months (3years)?
meg
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formula to calculate the monthly repayments of this contract

I know that the interest rate is constant through the whole period and the interest method is declining balance. By declining balance mean that the interest at period t is calculated on the balance of period t. In the table below, interest of the…
DJJ
  • 133
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How can Capital Market Line portfolios be efficient when they're not feasible?

My course notes define Suppose now that there are many different investments $A_1,\dots,A_n$ available. We can invest our one unit of currency by investing $t_i$ in $A_i$ for each $1 \leq i \leq n$ as long as $\sum_{i=1}^n t_i=1.$ What are all…
mjc
  • 2,249
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Proof that effective annual interest rate increases with compounding period

The effective annual interest rate (EAR) is given by: $1 + EAR = (1+\frac{APR}{k})^k$. I want to show that this expression is increasing in k for positive k. Differentiating leads to the key inequality: $ln(1+\frac{APR}{k}) \geq…
SWF
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How to calculate the pips per value in Forex

I am trying to fully understand the logic behind Forex calculations. However I find myself stuck on some parameters. Let me explain better with a real example of a trade: Pairs: AUDUSD Date Open: 15 June 2023 Entry Price: …
Bruce Ecurb
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Are these both compound interest formulae?

Given $i$ the annual interest rate expressed as a decimal, $P$ the principle value and $F$ the future value. If I want to compound my interest $n$ times per year for $t$ years what is the difference between the following two methods…
Kantura
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Expected present value and expected future value

Suppose that the interest rate $r$ is a random variable. Given a future value $FV$, the expected present value is $\mathbb E (\frac{FV}{1+r})$. Given a present value $PV$, the expected future value is $\mathbb E ((1+r)PV)$. What's with the…
Bunbury
  • 395
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Convexity of a zero bond

Now we know that the bond price formula is : \begin{equation} \label{eq1} P = \frac{c}{(1+y)^1} + \frac{c}{(1+y)^2}+\cdots + \frac{c+P_p}{(1+y)^T} \end{equation} or equivalently : \begin{equation} P= \frac cy \left[1-(1+y)^{-T}\right] +…
Homer Jay Simpson
  • 380
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Portfolio value on selling and buying calls

Consider buying a call option with strike $K − δ$, selling two call options with strike $K$ and buying a call option with strike $K + δ$, where $K, δ > 0$ and $K > \delta$, all with maturity $T > 0$. Draw the terminal payoff function of this…
Bing Bong
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