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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Disbursing $500,000 over 240 months at an interest rate of 3.5%

I'm trying to determine what the monthly payouts would be based on the following information. Starting Amount: $\$500,000$ Interest Rate: $3.5%$ monthly Deplete over $20$ years ($240$ months) How much will be disbursed from this account each month?…
Dr RobotNick
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Calculate the amount if 20,000 is compounded annually for 2 years and 4 months @12% p.a.

Calculate the amount if 20,000 is compounded for 2 years and 4 months @12% p.a. I try solving this problem but my answer was wrong. We apply formula, $A = P(1 + R)^n $ $= 20,000(1 + .12)^{2 + 4/12}$ $= 20,000(1.12)^{2.3334}$ Calculating this on a…
user1055431
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How to solve an equation for ‘r’ if it both exists at the numerator with exponent and the denominator?

I’m solving some finance problems and faced the equation below. $$PV = C(\frac{1-\frac{1}{(1+r)^n}}{r}) + \frac{FV}{(1+r)^n}$$ Since I don’t have the finance calculator, I want to solve that for r in hand. Assume all PV, FV, n, C are constant. Is…
Joseph Hwang
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Portfolio Optimization: Sharpe Ratio with two equally weighted assets

I have an exercise: Suppose that µ1 = 5%, µ2 = 3%, σ1 = 35%, σ2 = 20%, κ = 40, w1 = 0.5, w2 = 0.5, rf = 1%. What is Sharpe Ratio of the given portfolio? Applying this function: I get this: But the correct answer given is: 0.128358764952167 Can you…
Irmantas Želionis
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How would I re-write a mortgage equation to solve for the APR, knowing the weekly payment?

I'm playing around with Australian house sales and rental data, and I've noticed that over the last couple of years, more than half of all renters are paying more than the entire owners mortgage (in March it was 77%, and so far this month a whopping…
OceanHydro
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Calculate effective rate of the loan - additional fees

I am having following parameters: loan_value = 20000 Annual rate = 2.9% other fees = 500 periods of repayment = 24 (2 years, each month) additional fees per month = 2 now, given the formula: EIR = loan_value * (1+Annual rate/24) power (periods of…
filtertips
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Interest Calculation

A university student receives his statement for his tuition and notices that he doesn't have enough money to pay it all off at once. The student inquires about interest rates at his university and is told the following information: You will be…
Sujaan Kunalan
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How to calculate APY from APR?

I'm trying to figure out how some investments based on compounding interest with bi-weekly contributions compare. One lists the APY, and the other lists the APR. I'm writing a program for comparing multiple interest rates, and want to make sure my…
ZeroPhase
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Real world asset acquisition problem with two or more unknowns who are interdependent.

I am trying to create a calculator that allows users to specify asset classes (e.g. 500 in fund1, 500 in fund2, etc.) and the desired fraction of the total portfolio per asset class (e.g. 70% in fund1, 30% in fund2). The equation should determine…
Koen
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How much should I apply monthly, starting TODAY, to get $20000 in 36 months, considering an interest rate of 20% per year?

$n = 36$ $FV = 20000$ $r = 0.20$ per year or $\approx$ $0.0153$ per month $PMT =$ ? Question: What type of cash flow is this? I know the first payment starts in $t = 0$, so, I think the formula I should apply to this is: $$FV =PMT \times (1+r)…
Corvo
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Compound interest problem

Question: A sum of money becomes 16 times of itself in 2 years if compounded half yearly. How much time it will take to becomes 27 times if compounded yearly. (A) 2 years (B) 3 years (C) 4 years (D) 6 years My approach:- $$P(1+R/200)^4 =16P$$ which…
Fin27
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Payoff of a Contract

Let $S$ be the value of a stock that evolves according to $dS$=$\mu$$Sdt$ + $\sigma$$SdB$. A contract has a payoff at expiration of $V_T$=$(S_T)^3$. What is the value of $V_0$ of the contract at $t=0$? Express your answer in terms of $r, T, \sigma,…
Hector Lombard
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Sinking fund to pay off Mortgage

Wanda takes out a 28-year mortgage for $192000 at an interest rate of j_1= 7.8%. After the 10th monthly mortgage payment, she decides to make some changes. To repay the loan, she will make 90 more mortgage payments (additional to the 10 she has…
Zain
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TVM solver - Find rate if compounded quarterly

I am trying to solve Question 8 using the TVM solver. The question is pretty straightforward and they ask to find the rate. I'm not sure what I did wrong, I put the following values but still not getting the right answer.
Simran
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Query about ROI and Annualised Interest

I would appreciate an explanation or example so I can wrap my head around this problem. Consider an asset that costs \$10,000. In 3 years it generates \$40,000, but it has to be replaced every 3 years. So, in a 3-year time horizon, the ROI would be…
KP7
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