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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Amortization with skipped payments

Amortization is usually calculated with the formula And if graphed in excel So my question is how would it be to solve for the payment of the 10th payment or year if in the presented sheet, the eighth and ninth monthly payment would be skipped and…
Tomy
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Finding accumulation function given force of interest

An investment grows at a force of interest $\delta(t)= \frac{3\sqrt{t}}{100}$. Calculate the effective annual rate of interest over $4$ years. $a(t)=e^{\int_0^t \frac{3\sqrt{t}}{100}…
Tosh
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Annuity at nominal rate

Consider a $30$-year loan of $200,000$ that can be repaid with $A$ per month at a nominal rate of $10$%. Calculate $A$. Effective monthly interest rate is given as $\frac{0.1}{12}$ Present value of loan is given as $200 000=A…
Tosh
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3 year structured deposit

A bank has launched a three year structured deposit that offers an effective rate of interest of $8$% perannumfor the first $18$ months, $1.5$% per quarter for the next 6 months and $2$% per half year for the last 12months. If I wish to accumulate…
Tosh
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A monopolist can produce any level of output at a cost of $\$10$

In one market, the demand is $D_1=80-P_1$ and in the other $D_2=100-2P_2$. Suppose the markets are separated. What output level should be produced and what price will prevail. Since $D_1=80-P_1$, then…
stackdsewew
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Interest deposited before it is calculated

I have an array of periods, with the number indicating a balance at the end of the corresponding period. For example, balances: [0, 0,-10, 0, 0] indicates that at period index 2, the balance is -10. When the balance is negative, there is an…
CMont
  • 111
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The lower bound for the prices of European call options with respect to discrete strikes

We observe Euro-call option prices at discrete strikes, say, $C_1>C_2>C_3...$ at several strikes $K_1
Jingjings
  • 295
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Calculating the principal

By which formula shall I calculate the amount for the following problem: Let say I want to buy a product, for which, I need to pay monthly installment of Rs500 , for 3 Months and rate of interest is 12% per annum. The amount which needs to be…
xyz
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How to calculate the cost of debt

The bonds of ABD Ltd have a face value of $1000$ with one year remaining to maturity. The bonds pay coupons at the rate of $10\%$ p.a. If the current market price of the bonds is $1018.50$, what is the firms cost of debt? I know that the annual…
jason
  • 91
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Present values with denser discounting

With an annual interest rate of 10%, the present value of 100 dollars received one year from now is $PV = \frac{100}{1.1}=90.91$. If instead the 100 dollars is received in two installments of 50 dollars and the first payment is made 6 months from…
puk300
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Value price of Bond

Hi, can you help me with this exercise ? I'm good in maths but don't understand these financial problems. I would be grateful for any help One morning, Mr. Kowalski purchased a two-year bond with the face value of $1,000, the coupon rate qual to 10%…
Michael
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Mortgage amortization schedule issue

I wrote a program that does a mortgage schedule. When comparing it with other online sites that are doing the same calculations I seem to be off $0.01 on every payment except the first. Here is an example: Loan Amount: $398,483 Interest rate:…
null_pointer
  • 101
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Interest re-invested given Force of interest

Jason deposits $3960$ into a bank account at $t=0$. The bank credits interest at the end of each year at a force of interest $\delta_t=\frac{1}{8+t}$ Interest can be reinvested at an annual effective rate of $7$%. The total accumulated amount at…
Tosh
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Net present value given cash flows for 2 different projects

Project P requires an investment of $4000$ at time $0$. The investment pays $2000$ at time $1$ and $4000$ at time $2$. Project Q requires an investment of X at time 2. The investment pays $2000$ at time $0$ and $4000$ at time $1$. The net present…
Tosh
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2 answers

question on force of interest with investment at 2 different times

You invested $500$ on Jan $1$ $2012$. To save for this amount, you invest $x$ on Jan $1$ $2008$ and $2x$ on July $1$ $2008$. The force of interest is $\delta_t=0.02t$ where $t$ is $0$ on Jan $1$ $2008$. Find $x$. The accumulated value at…
Tosh
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