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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Which Option is more expensive?

Consider two European put options, written on the same asset, with the same maturity, but different strike prices: K1< K2 Which option is more expensive? Then Answer the same question, but using call options instead. It made sense to me that a put…
Andy
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How to find rate of depreciation in this problem?

The value of a machine is estimated to be 27,000 at the end of 1994 and 21,870 at the beginning of 1997. Supposing it depreciates at a constant rate per year of it's value at the beginning of the year, calculate: 1) Rate of depreciation 2) The value…
Nirvan
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Trouble understanding the constant before an increasing/decreasing annuity.

I have this question here that I'm having trouble understanding An annuity immediate has semiannual payments of 800,750, 700,..., 350 at $i^{(2)}$ $= .16$ if $a_{\overline10|.08} = A$, find the present value of the annuity in terms of A The…
user334683
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Future value given force of interest

Find the future value of a five year annuity ($s_{(n)}$) if $\delta _t=0.02t$ for $0 \le t \le 5$. What I know is $\delta_t= \frac{A'(t)}{A(t)}$ $A(5)=\frac{0.02}{0.02. X5}=0.2$ I am not even sure of this. And then I do not know know to proceed…
Tosh
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Finding the present value of the given cashflow.

A loan is repayable by an annuity certain , which is payable annually in arrear for 16 years and calculated at effective rate of interest $5\%$ pa. The payments at t=1 , t=2 , t=3 , t=4 , . . . . . . t=15 , t=16 are given as : (100 , 100 , 120 ,…
User9523
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Reinvesting and accumulated values

I'm having trouble understanding the solution for this problem Susan invests Z at the end of each year for seven years at an effective annual interest rate of 5%. the interest credited at the end of each year is reinvested at an annual of 6%. The…
user333888
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arbitrage and exchange rate: Find x if $(1-t_c)*S_f*(1-t_c)*(\frac{1}{S_f+x})<1$

Okay, so I need help with this math problem. The professor said the answer is $x=.000307785$ I need to find x if: $$(1-t_c)*S_f*(1-t_c)*(\frac{1}{S_f+x})<1$$ $t_c=.02\% $ and $S_f=1.3000$ The answer I am getting is $x>-0.000519948$ if I change…
geeking4math
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Repayment of a loan with non level annual payments

A loan of $10,000$ is being repaid with 20 non-level annual payments. The interest rate on the loan is an annual effective rate of$6$% . The loan was originated 4 years ago. Payments of $500$ at the end of the first year, $750$ at the end of the…
Tosh
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Amortization varying series of payments

Having trouble understanding the solution for this question. 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 $200, at the end of the second year…
user270494
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How to find the interest rate?

Lets say we have this following scenario: 1000000 = 1000 * (1/r) * [1-(1/(1+r)^43)], where PV=1000000, n=43, C=1000, r=? We have to find "r", so how do we manually go about finding "r"? I know "r" can be found by using a financial calculator but I…
SAR
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2 answers

Annuity payment formula

Here is the problem. I want to take loan of $24{,}000$\$, and I want to repay it in series of equal payments monthly in time of five year. I use this formula to get the monthly annuity $$ \operatorname{P}=…
Negra
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Outstanding balance and amount of interest

I'm having trouble with this problem: A loan is being repaid with level annual payments based on an annual effective interest rate of $8\%$. If the outstanding balance immediately after the $10$th payment is $1000$, calculate the amount of…
user270494
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2 answers

Amortization vs Sinking Fund Financial Mathematics

I'm struggling with this question A 20-year loan of 20,000 may be repaid under the following two methods: i) amortization method with equal annual payments at an annual effective rate of 6.5% ii) sinking fund method in which the lender receives an…
user326594
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Sinking fund and differing interest and payment periods

I'm having trouble understanding this solution for a sinking fund question. A borrower takes out a loan of $2000 for two years. Construct a sinking fund schedule if the lender receives 10% effective on the loan and if the borrower replaces the…
user270494
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Is the price of a European option at time $1$ equal to the payoff at time $1$ if expiration is time $2$?

$S(0)=150, u=1.2, d=.8, X(\text{strike price})=120, r=10\%$, expiration $T=2$ where $S(t)$ is price of stock at time $t$, $S_u$ is price of stock if it goes up at time $1$ and $S_{uu}$ is price of stock if it goes up again at time $2$, similar for…
idknuttin
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