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

2
votes
1answer
54 views

CI for the expected value of the sum of two dependent normal RVs

Let's consider 2 dependent, normally distributed R.V.s, $X_1$ and $X_2$. The means, $\mu_1$ and $\mu_2$ are known, as well the covariance matrix $\Sigma$. Let's consider the following random variable:...
0
votes
2answers
65 views

Basic annuity loan problem

I've got a loan of $\$32000$, which I need to repay in $36$ monthly payments, with annual rate of $10\%$. What is the amount of monthly payment, which I need to pay? There will be $36$ payments, thus ...
0
votes
1answer
52 views

Reinvestment using $(Is)_{\overline{n}\rceil i}$… calculate $i$

I am working on the following problems which should not involve a difficult polynomial, but I tried a couple of times without success. Victor invests $300$ into a bank account at the beginning of ...
1
vote
1answer
40 views

Using $(Da)_{\overline {n} \rceil i}$ or $(Ia)_{\overline {n} \rceil i}$ in this problem?

I am trying to solve the following increasing (decreasing?) annuity problem from exam FM. A perpetuity costs $77.1$ and makes annual payments at the end of the year. The perpetuity pays $1$ at ...
0
votes
1answer
44 views

Using $(Ia)_{\overline {n} \rceil i}$ from Exam FM.

I am trying to solve the following problem which I am having a bit of trouble with. Olga buys a 5-yr increasing annuity for $X$. Olga will receive $2$ at the end of the first month, $4$ at the end ...
0
votes
2answers
255 views

Geometric progression in annuity

I am working on the following problem that involves annuity which deposits form a geometric progression. Stan elects to receive his retirement benefit over $20$ years at the rate of $2,000$ per ...
1
vote
0answers
356 views

Calculating the interest rate for an annuity (Exam FM)

I have been searching for a way to solve for the interest rate given the monthly payments of a loan. I would like to set up a problem as the following. $X$=monthly payment , $i$=effective ...
1
vote
0answers
44 views

Finding drop payment with varying interest rates..

Person A is accumulating a 10,000 fund by depositing 100 at the end of each month starting September 1,2002. If the nominal interest rate on the fund is 12% convertible monthly until May 1,2005, and ...
0
votes
1answer
65 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
60 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 ...
2
votes
1answer
224 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
315 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
51 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
92 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
201 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
48 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
36 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
1answer
189 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
70 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. ...
1
vote
1answer
46 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 account ...
1
vote
1answer
586 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
48 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
125 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
30 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
965 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
61 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) = \ln({1+i})(...
0
votes
1answer
27 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
113 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
40 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
31 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
88 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 ...
2
votes
2answers
278 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 https://www.cs.princeton.edu/courses/...
1
vote
1answer
118 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
132 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
66 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
61 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
127 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
25 views

Help on understanding tax bracket computation

Warning: some codes Tax Bracket: 1 up to 5,070 ---- 10% ...
1
vote
2answers
72 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
34 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
213 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
91 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
126 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
130 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
30 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
73 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
76 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 $$ \frac{1}{2}\sigma(x)^2x^2\frac{\...
1
vote
1answer
36 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 ...