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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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Amortization table does not match formula

Using the formula $\dfrac {\log \left(1+\frac {Br}{P(1+r)} \right)}{\log (1+r)} = n$ from https://math.stackexchange.com/a/2101796/164710, with values B = 10000 r = 5% (0.00416667 monthly) P = 250 I get 36.93 periods (months), but when I calculate…
Ralph
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Rearrange amortisation formula to find interest

I'm struggling to rearrange the amortisation formula of a loan to find the interest rate when the other variables are known. I.e. rearrange $$A = \frac{i \times P \times (1+i)^n}{(1+i)^n-1}$$ To find $$i = ...$$ Where A = payment amount per period i…
Cheesecake
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Accumulation of a series of payments

A loan is repayable by eight annual payments, starting in one year's time with an interest rate $i$. Payments one to three are half as much as payments four to eight. What is the accumulated value of payments one year before the end of the eight…
james1395
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A problem from FM exam on accumulation and amount function, please help!

Suppose that accumulation function $a(t)$ is differentiable and satisfies $$a(s+t)=a(s)a(t)$$ for all nonnegative real numbers s and t. $a'(t) = a'(0)a(t)$. Show that $a(t) = (1+i)^t$, where $i=a(1)-a(0)=a(1)-1.$ I concluded that from…
user3000482
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Investing: Rule of thumb/formula to get a sense of Net Present Value given two different rates of compunding..

I'd like to know if there is a rule of thumb or formula that one can use to get a rough sense of the net difference between the end value, given two different compound interest rates, different principles and the period of compounding which is…
Mani
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Dothan's model - expected value of $B_t$

Let's consider Dothan's model of the short-time interest rate: $$d r_t = \mu r_t dt + \sigma r_t dW_t,$$ where $r_0 = r$, $\sigma>0$, $\mu \in \mathbb{R}$. Prove that: $\mathbb{E}(B_t)= \infty$, where $B_t$ is the banking account process. My first…
Elizabeth_Banks
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Finance - Present Value of Perpetuity

I'm having trouble solving this perpetuity problem Assume this is the case for a hypothetical company that is expected to pay half-yearly dividends of $0.20$ forever, with the first dividend payable in six months’ time. If you purchased the…
Joshua Alexander
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find the value of a loan with hp12c

I can't seem to resolve this problem with hp12c. You made a loan with 1,2% tax per month. You can pay it in two times: 125000 after the 10th month and 45000 after month 16th. They ask for the value of the loan, so I put 125000 PMT; 45000 PMT; 1,2…
Tomb
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Financial Mathematics Reducing Balance

I am struggling on a financial mathematics question in a practice paper. The question is: Mr Bakele owns a courier company. His first truck costs R550 000 and it depreciates 35% per annum on a reducing balance, In 4 years the truck must be replaced.…
Nicole Carr
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Solve for n in Compound Interest Formula

I would like to solve the compound interest formula $$V = Pz^n + c\left(\frac{z^{n+1}-z}{z-1}\right)$$ for $n$. Or, given what I would like the final value to be, the amount I can save a year, an interest rate, and how much money I have to invest…
David Beck
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Calculating accumulated value of an investment account

$30,000 is invested at the start of each year for the next 20 years. The money invested earns interest at an annual effective rate of 4%. The interest earns interest at an effective rate of 2% a year. If all interest payments are made at the end…
user377161
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Compound interest calculation for mortgage

I've been frying my brain over a mortgage comparison for a house I'm buying. It comes down to what I hope is a simple maths problem to someone who is actually good at maths, unlike me. 1) Mortgage A has a fixed interest rate of 1.89%. This mortgage…
Andre
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Loan repayment, finding $n$

How long will it take to pay off a debt of $5000$, with an annual interest rate of $19\%$, compounded monthly, if you make a monthly payment of $100? I've been using the Loan Repayment formula, where I look for the value of n. So far I have: $$100=…
Arizona Lee
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Loan Payment : Charging fixed amount against remaining balance?

The formula for calculating the payment amount $P$ for a loan payment is well established: $$B_n = A (1+i)^n - \frac{P}{i} [(1+i)^n - 1 ]$$ where $B_n$ the balance after $n$ payments, $A$ the principal and $i$ the interest charged monthly. This…
Marcel
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How can I calculate maximum Loan amount?

I want to calculate max loan amount a client can get having this info: loan terms in years Interest Rate Percentage Max Monthly payment The loan Interest calculation is semi annual compounding I have used this formula: termInMonths = termInyears *…
Besat
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