Mathematics Stack Exchange
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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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Promissory note selling to the bank before due date.

Bob signs a promissory note to repay Linda $\$9000$, with the note due in 11 months from January 14, 2013. The maturity value of the note is $\$9544.55$. Linda sells the note to a bank on April 18, 2013. What price does Linda get for the note if the…
adamvincent
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Best way to pay off multiple loans to mitigate accrued interest...

I have 3 separate student loans with varying interest rates: $2,380 at 4.66% $5,500 at 4.29% $7,000 at 4.29% Interest compounds daily, and the loans are set to amortize over 10 years, with 12 payments per year. This comes out to roughly $156.24…
Derek Andre
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Artitrage-free family of bonds

Which of those processes indicate an arbitrage free family of bonds in terms of r? $T^*=1$. The process $r_t$ is given by: a) $r_t = 1$ for all $t \in [0,1]$ b) $r_t = B_t$ for all $t \in [0,1]$ c) $r_t = B_1$ for all $t \in [0,1]$ d) $r_t = t +…
Elizabeth_Banks
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Assistance on whether numbers are correct? Financial mathematics annuities problem

You would like to have $750,000 when you retire in 25 years. How much should you invest each quarter if you can earn a rate of 4.2% compounded quarterly? a) How much should you deposit each quarter? b) How much total money will you put into the…
onlyZoe
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Formula to calculate amortization schedules on daily rate loans

I am trying to understand how amortization schedules are created. While i can find some information based on monthly and yearly rates, I cannot find any that show how to calculate schedules based on a daily rate. By way of example... If I want to…
JoeGeeky
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APR Problem - How much finance should I take out based on a credit of £550?

I'm having a problem putting my mathematics degree to good use. A friend of mine wants me to work out the following problem for him: A motorbike costs £14,000. I will receive a "sweetener" from the motorcycle company of £550 if I take out any amount…
Doug
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Mary got a loan with a monthly fee of 1%, how much did she have after 6 months? Solving this problem 2 different ways.

Mary got a loan of 1000 euros. The institution that made the loan charges a monthly fee of 1%. Because, in the following 6 months, Mary has done no amortization of the loan, how much does she owe to the institution after those 6 months? I…
Mark Read
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how long would a short term investment last?

I need to compare two kinds of payments of a 750k debt. The first consists of 300k each year for 5 years. The second offers 20% discount (pay 600k) if payed at sight but then, I'd have to make a loan to have 600k (PMT = 246.348,93 for 5 years, or…
Tomb
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Correct way to convert interest rates

Let's assume $r_{360,sa}$ is a zero coupon rate compounded semi-annually, under act/360 day count. I'd like to convert it to zero coupon rate compounded annually, under act/365. Is the below conversion…
luka5z
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How to calculate group finance with donations

There is a group of 15 people, living together for one week. Different people paid some amount to buy food items, so they had expenditure of €163 as group. They eat breakfast and dinner everyday, but not everyone consumed each meal (for reasons like…
netzaffin
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What is the total inflation rate over a several year period given the each year inflation rate?

Consider a given inflation rates $I_1, I_2, \dots, I_N$ for years $1 \dots N$. What is the total (cumulative) inflation rate over the whole period of $N$ years? I was trying to chain-link the resulting purchasing powers: $P_1=P_0\frac{1}{1+I_1}$,…
mbaitoff
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Proof Regarding Effective Annual Rate Inequality

I tried to use the $$\lim_{m \to \infty}(1 + \frac{i}{m})^{m} = e^i$$ as a starting point but couldn't work it out quite right. I am using the definition that the EAR is $$(1 + \frac{i}{m})^{m} - 1$$
Rebecca
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Level annuity payable monthly

A loan of £10,000 is to be repaid over 10 years by a level annuity payable monthly in arrears. The amount of the monthly payment is calculated on the basis of an interest rate of 1% per month effective. Find the monthly repayment, the total capital…
Goshawk
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Price of a Bond

I am working through an example in a textbook and, for the life of me, cannot figure out how they got from one step to the next. Here's the example: A bond of 500, redeemable at par after 5 years, pays interest at 13% per year convertible…
Carolyn
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college finance

The HBO co. is raising \$150,000 in 30 months by making monthly deposits which can be invested at 6%(12). Assuming they withdraw \$150,000 a month after the last deposit. If they deposit \$R per month for the first 10 months, \$2R for the next 10…
manny singh
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