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.

If you don't think your question is suited for this site, try:

2637 questions
0
votes
1 answer

Forward Contracts.

Let $K$ be the forward price of a contract/asset agreed at time $t=0$ to be paid at $t=T$. Now, we say that the forward price $K$ is determined in such a way that the ' value of the forward contact ' at $t=0$ is zero. Can anyone explain the…
User9523
  • 2,094
0
votes
1 answer

Financial mathematics perpetuity problem

I'm having trouble solving this FM problem. For $3000$, Nick purchases an perpetuity-immediate paying $100$ at the end of each $6$ months period. For the same amount and for the same effective annual rate Paul purchase an annuity-immediate with…
user270494
  • 687
0
votes
2 answers

Annuities and interest conversion

I am having trouble understanding how to find the equivalent rate of interest per payment periods for annuities. For example, for this question: Find the accumulated value at the end of four years of an investment fund in which 100 is deposited at…
user270494
  • 687
0
votes
1 answer

IRR for Incremental Investment Doubt

I had a doubt in the following question's solution: Aren't the signs in the equation wrong? Shouldn't it be $-(6,000,000 - 400,000) + 15,000,000(P/F, i^*,15) - 400,000(P/A,i^*,14) = 0$ (using negative signs for cash outflows (disbursements) and…
Leponzo
  • 395
0
votes
2 answers

Nominal annual interest

A bank offers the following certificates of deposit: $$ \begin{array}{c|lcr} \text{Term in years} & \text{Nominal annual interest rate(convertible semi-annually)} \\ \hline 1 & 0.05 \\ 2 & 0.06 \\ 3 & 0.07 \\ 4 & 0.08 \\ \end{array} $$ The bank does…
Tosh
  • 1,614
0
votes
0 answers

Find the value of forward contract

The current spot gold price is $\$1788$ per ounce. The storage cost is $\$24$ per ounce per year, to be paid quarterly at the beginning of each quarter. Suppose the current $3$-month and $6$ month spot rates are $0.15\%$ and $0.20\%$ (both are…
Jerome Cheang Yue Liang
  • 71
0
votes
1 answer

Finding implied interest rate from swap exchange

Suppose the current term structure of interest rates (0.5 year, 1 year, 1.5 year, 2 year maturities annualized with semi annual compounding) is (5.00%, 6.00%, 7.00%, 8.00%). A 2-year vanilla interest rate swap having a notional principal of…
Jerome Cheang Yue Liang
  • 71
0
votes
1 answer

Financial mathematics - earning compound interest

This I assume is a very simple question but can't really wrap my head around it. So the question is: If 100 dollars is deposited at time t = 0 into an account earning 10% interest and $20 is withdrawn at t = 1 and 2, then how much can be withdrawn…
Timothy
  • 3
0
votes
1 answer

Future value and simple interest

On a loan of $3,000 at an interest rate of 12% per year when half of the loan principal is repaid as a lump sum at the end of four years and the other half is repaid in one lump sum amount at the end of eight years, and if the interest is not paid…
Gustav Magnusson
  • 3
0
votes
1 answer

Compounded discount rate

The total amount of a loan to which interest has been added is $20000$. The term of the loan was for $4.5$ years. If the annual rate of interest was $6\%$ and interest was compounded annually, what was the amount of the loan? The answer is $15…
Tosh
  • 1,614
0
votes
2 answers

Present value and discount function

What deposit made today will provide for a payment of $ \$1000$ in $1$ year and $ \$2000$ in $3$ years, if the effective rate of interest is $0.075$. Answer is $\$2540.15$ I have calculated $d=0.069$ by using $i=\frac{d}{1-d}$ Then by using…
Tosh
  • 1,614
0
votes
2 answers

Compound interest with penalty in withdrawal amount

Carl puts $10000$ into a bank account that pays an annual effective interest rate of $0.04$ for $10$ years. If a withdrawal is made during the first five and a half years, a penalty of $5\%$ of the withdrawal amount is made.Carl withdraws $K$ at the…
Tosh
  • 1,614
0
votes
1 answer

Models for Financial Economics: Determining The Amount to Lend in Synthetic Assets

You are given: (i) The price of a stock is 43.00$ (ii) The continuously compounded risk-free interest rate is 5% (iii) The stock pays a dividend of 1 three months from now (iv) A 3-month European call option on the stock with strike 44 costs…
Seraphim
  • 709
0
votes
1 answer

Finding the accumulated profit.

The above project is financed by a loan. The company pays 6.25% on the money borrowed and earns 4% on money invested in its deposit account.(Spare funds can't be used to repay the loan at any time) Cashflow can be understood as : (1) At the start…
User9523
  • 2,094
0
votes
3 answers

interest being compounded annually

What sum would amount to 31,104 in three years at 20% p.a Compound interest, interest being compounded annually ? (Ans: 18,900) Solution: \begin{align*} C I &= A – P \\[1ex] P &= 31104 – P\left( 1 + \frac{20}{100}\right)^3 \\[1ex] P &= 31104 –…
Alfred Jerome
  • 3
1 2 3
…
52 53