Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

learn more… | top users | synonyms

0
votes
1answer
52 views

need help calculating the interest “i”

A regular deposit of 120 dollar made at the beginning of each year for 20 years. Simple interest is Calculated at a rate of i per year for 22 years. At the end of the 22-year period, the total ...
1
vote
1answer
49 views

Annuity/Finance

I'm trying to determine the question below: Mr. Learnwell wants to setup a scholarship of $4500 paid at the end of every six months. If the interest rate is 6.4% compounded semi-anually, how much ...
0
votes
2answers
312 views

current value of a forward contract

Suppose we hold a forward contract on a stock with expiration 6 months from now. We entered into this contract 6 months ago so that when we entered into the contract, the expiration was T=1 year. The ...
2
votes
1answer
56 views

Annuity problem, calculating the accumulated value.

the following is the problem I am trying to work on. Kathryn deposits 100 into an account at the beggining of each 4 year period for 40 years. The account credits interest at an effective annual ...
-2
votes
1answer
73 views

Sunk Costs NonRefundable Deposit

A young couple has made a nonrefundable deposit of the first month’s rent (equal to 1,000 dollars) on a 6-month apartment lease. The next day they find a different apartment that they like just as ...
0
votes
1answer
43 views

Hard to understand the strategy of the following investment.

Upon attempting to solve a problem regarding annuities, I am a little puzzled regarding the following strategy of investment. $10,000$ can be invested so that one can purchase an annuity-immediate ...
0
votes
2answers
54 views

Annuity problem from Exam FM

I am working on the following problem and I was wondering if someone could help me solve it. Chuck needs to purchase an item in 10 yrs. The item costs $\$200$ today, but its price inflates $4\%$ ...
1
vote
1answer
105 views

books on the application of linear algebra on statistics/finance/machine learning

I am reading "linear algebra done right" by Axler and like it a lot. One thing though, in the end I would like to put these theory to use and as a math textbook it doesn't cover much application. ...
2
votes
2answers
41 views

Identity of $I_t$ under annuity with principal $1$

I am trying to prove an identity and quite not get there. The following is the premise. One deposits $\$1$ at time $t=1,2, \cdots ,n$. evenly spaced. The effective interest per payment is $i$. ...
0
votes
1answer
27 views

Is there a mistake with this national income model Mik. Wisniewski Intro to Math Methods in Econ pg. 61

I can't figure out the steps to this equation for the national income model. It seems simple, but I don't see why in step 4 I don't get Y-bY+tY I thought it was a mistake in the book at first, but ...
1
vote
0answers
32 views

Black and Scholes solution

Consider the Black and Scholes equation. What is the (financial) interpretation of the solutions S and $e^{rt}$? They both satisfy the equation.
1
vote
1answer
59 views

Mortgage payment calculation without annuty.

I have been asked the following problem by a student of mine and there is a specific method that he requested. A mortgage of $\$450,000$ is loaned for a monthly payment for $30$ years with nominal ...
2
votes
1answer
69 views

Intuitive understanging of re-investment.

There was an interesting problem that I would like to have some input from people who knows a bit of finance. The following is the situation. Smith loans $\$10,000$ for $i=5\%$ for $10$ years. ...
0
votes
0answers
79 views

Calculate monthly payment and effective interest

I asked this on StackOverflow first because I'm using JavaScript, but there's nothing really wrong with the script only the algorithm so I'm trying here instead: I'm building a calculator for a car ...
1
vote
1answer
39 views

Question regarding interest method during a year. $i-\delta$

B and P deposits the amount $100$ in separate bank accounts. B's account have a nominal rate convertible semiannually. P's account has a force of interest $\delta$. After $7.25$ years, each ...
1
vote
1answer
160 views

Force of interest problem from Exam FM

Tawny makes a deposit into a bank account which credits interest at a nominal interest rate of $10\%$ per annum, convertible semiannually. At the same time, Fabio deposits $1000$ into a different ...
0
votes
1answer
38 views

Force of interest :$e^{\int_0^t{\delta_t}ds}$ vs $(1+\frac{i^{(2)}}{2})^2$

I was wondering if someone could help me confirm the answer for the following problem regarding force of interest. X deposits $1$ at time $t=0$ with force of interest $\delta_t=\frac{t^2}{k}$. Y ...
0
votes
1answer
84 views

182-Day T-Bill vs. 91-Day T-Bill

I am trying to understand how T-Bills work and it would be great if someone could explain me using the following question At $t=0$ Smith buys a 182-Day T-Bill with a simple annual discount rate of ...
0
votes
1answer
25 views

“Cost per Lead Quality” Score

I'm a marketing manager and would like to calculate a cost per lead quality "score." I run a number of marketing campaigns, and I've figured out how to calculate a quality percentage for each campaign ...
0
votes
1answer
167 views

Discount rates vs. Interest rate problem.

I am working on a problem as follows. A discounted value $X$ that is due when $t=0.5$ has a present value \$4992. Calculate the value of $X$ when a), the effective annual compound interest rate ...
0
votes
1answer
38 views

Finance problem - Canadian bond with simple interest

I am having trouble understanding a lot of things from the following problem. It would be very helpful if I could get some explanations. Smith purchases a Canadian bond for 1000 with an issue ...
0
votes
1answer
23 views

Problem regarding Investments and selling the right.

I have trouble solving the following problem algebraically. Smith lends $\$1000$ to Jones at time $t=0$. Jones is supposed to repay Smith by paying $\$100$ at time $t=1$ and $2$, and $\$1000$ at ...
0
votes
2answers
37 views

Proof $(1+i)^t < 1+it$ if $0 < t < 1$

I am trying to prove that compound interests grow slower than simple interest in the first year. I attempted to do this with the following approach. Let $$f(t) = (1+i)^t$$ then $$f'(t) = ...
0
votes
1answer
24 views

Future value of investment with quarter payment

I'm a bit stuck on this problem, tried to solve it, but I don't know what is wrong with my way of thinking. A bank offers a deposit with the interest rate of 5% per annum with quarterly interest ...
1
vote
1answer
49 views

The meaning of “average annual compound rate”

I am currently working on this problem and I am having a hard time finding the right number. A mutual fund advertises that average annual compound rate of returns for various periods ending Dec 31 ...
1
vote
0answers
30 views

Finding the annual withdrawal, given initial and final amounts, and interest rate

I am working on the following problem and I keep getting a different answer. The principal $P=10,000$. The annual interest rate is $i=4\%$. The money is deposited at time 0 and the interest is ...
0
votes
1answer
23 views

Find the balance using Investment Year Method…

Here's the problem: Now, here is what I did: Since we invested $\mathbb{$}1000$ at the beginning of $1989,1990$, and $1991$, we find the balance of each contribution over the specified ...
2
votes
2answers
78 views

Are there other accumulation functions that holds $a(n-t)={a(n) \over a(t)}$?

This might be a beginner's question regarding accumulation methods and their functions, but so far I have learned that compound interest satisfy $$a(n-t)={a(n) \over a(t)}$$ Which allows nice ...
1
vote
2answers
116 views

Deriving Black Scholes using CAPM

I am referring to http://www.frouah.com/finance%20notes/Black%20Scholes%20PDE.pdf Section 3, which is a bit more detailed version of the original derivation from ...
1
vote
1answer
38 views

Calculate repayments amount on loan

I doing some work on a client website, however I'm finding it difficult to calculate the correct interest amount. I have the principle amount, for example £200 The loan is repaid over 3 months in ...
0
votes
1answer
60 views

Derivation of Efficient Frontier (portfolio optimization) question

In Robert Merton's derivation of the efficient frontier of a portfolio, he minimizes $\frac{1}{2}\sigma^2 $ over the investment weights in each asset, where $\sigma^2$ represents portfolio variance. ...
0
votes
1answer
41 views

Put-Call Parity

This question is from Pliska's "Introduction to Mathematical Finance" Suppose the interest rate r is a scalar, and let c and p denote the prices of a call and put, respectively, both having the same ...
1
vote
2answers
48 views

What is a discount?

I am learning some financial terms and am having trouble understanding what a discount $d$ is. Numerically, I understand that it is defined as $\frac{i}{1+i}$ but I do not intuitively understand what ...
0
votes
1answer
48 views

How to calculate total loan knowing only the APR, term and monthly payments?

I'm building a loan calculator with two different methods of user entry. One one side the user can enter their desired loan amount and specify a term and it will display the overall loan amount and ...
0
votes
1answer
20 views

Help on understanding tax bracket computation

Warning: some codes Tax Bracket: 1 up to 5,070 ---- 10% ...
1
vote
2answers
51 views

Present Value (Interest)

The question goes like this: What deposit made today will provide for a payment of 1000 in 1 year and 2,000 in 3 years, if the effective rate of interest is 7.5%? The answer given by the book is ...
2
votes
1answer
32 views

Saving for retirement - how much?

I'm working through a problem in the book "An Undergraduate Introduction to Financial Mathematics" and there is an example I can follow. The problem is: Suppose you want to save for retirement. The ...
1
vote
1answer
88 views

Recursive Solution to Interest with Monthly Deposits

I open an account at a bank with 1% interest compounded monthly. I'm adding $100 to it at the beginning of each month (starting with month 1). (a) Set up a recurrence relation for the amount in the ...
1
vote
1answer
46 views

Problem regarding equation of value and nominal discount…

Here's the full problem: Xiang and Dmitry are friends. They agree that Xiang will pay Dmitry $\mathbb{$}800$ immediately and another $\mathbb{$}200$ at the end of three years. In return, Dmitry ...
0
votes
1answer
70 views

Problem involving nnual dollar-weighted yield-rate on stocks…

Full problem: Arthur buys $\mathbb{$}2000$ worth of stock. Six months later, the value of the stock has risen to $\mathbb{$}2200$ and Arthur buys another $\mathbb{$}1000$ worth of stock. After ...
0
votes
1answer
84 views

Guess-and-check for annual effective interest rate and annual yield rate

Here is the full problem: Kurt loans Randy $\mathbb{$}14000$. Randy repays the loan by paying Kurt $\mathbb{$}4000$ at the end of one year and $\mathbb{$}6000$ at the end of two years and as well ...
0
votes
0answers
20 views

Does interest apply for the last month of an amortization?

I'm working out the loan repayments using the amortization formula $$\frac{\text{principal} \cdot \text{paymentPercentageInDecimal}}{1 - (1 + \text{paymentPercentageInDecimal})^{-\text{payments}}}$$ ...
1
vote
2answers
52 views

Amortize the debt problem

Monthly payments are made on 130000 dollars at 5% for 25 days. Determine the payment needed to amortize the debt.
0
votes
1answer
47 views

Solving Black scholes PDE using Laplace transform

I'm trying to obtain the Laplace transform of Call option price with repect to time to maturity under the CEV process. The well known Black scholes PDE is given by $$ ...
1
vote
1answer
34 views

Prove $\sigma_V=x\sigma_S$. (Financial Mathematics)

Prove that the standard deviation of the value $V(T)$ at time of any portfolio $(x,y)$ at time $T$ in a one-step binomial is given by $\sigma_V=x\sigma_S$, where $\sigma_S$ is the standard deviation ...
0
votes
1answer
34 views

Is there a way to do this? Fixed deduction for x rounds where total = fixed amount

I am trying to calculate the reduction amount / step per round for the given: rounds = 1000 points = 80 starting at reward = 1 point So from round 1 which has a reward of 1 point deduct a fixed ...
1
vote
1answer
51 views

Markov property question

In every book I can find, the Markov property for ito diffusions, $E[f(X_{t+h})\mid F_s] = E^{X_t}f(X_h)$ is stated for $\textbf{bounded}$ Borel functions. However, I have the following statement ...
3
votes
0answers
248 views

numerical method (implicit , backward difference or forward difference) for nonlinear pde

$\newcommand{\lbar}{\underline{\lambda}}$ In this linear PDE: \begin{cases} B_t+b^Q(r,t)B_r+\frac{1}{2}d^2(r,t)B_{rr}+(\mu(\lambda,t)+\alpha \sigma (t))(\lambda -\lbar)B_{\lambda} \\ ...
1
vote
1answer
24 views

Compound interest problem with increasing deposits

An Investor starts with an initial investment : $A$ He earns a steady profit of 10 percent per year. But every year he adds additional amount which increases by 15 percent every year. At the end of ...
0
votes
0answers
43 views

Reverse Engineer Math(financial) Answer.

I'm starting to question the Payment amount generated by the software my lender is using, but it could be my calculations that are wrong. I would like confirmation before I proceed. Is my approach ...