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

1
vote
1answer
104 views

What does it mean to be an equivalent repay scheme? (sinking fund vs. amortization)

I am having trouble solving the following problem which seems simple, but I cannot quite get it right. Smith can repay a loan $L=250,000$ in one of two ways 1), 30 annual payments based on ...
0
votes
2answers
92 views

annual and effective annual interest rate

Can anyone help me to find the answer to the question below? I am taking the Engineering Economics exam and need to be sure about the correctness of my answer. Here is the question: Smart Visa, ...
2
votes
0answers
35 views

How to calculate present value with changes interest

How to calculate present value with period of 5 years and 6 months? Besides that, there is interest changes and compounded differently. Is there any formula?
0
votes
1answer
19 views

$\frac{L}{a_{\overline{n}\rceil i}}(n-a_{\overline{n}\rceil i})$ vs. $Li \frac{n-1}{2}$ which is larger?

I am having trouble deciding which of the expression is larger. The following is the original problem and I may not have the expression entirely correct, but I am pretty confident. A loan of $L$ ...
0
votes
1answer
14 views

Reinvestment calulators

I was wondering if someone can direct me to, or explain, calculations regarding reinvestment. For instance, say your initial investment is \$15,000, and via investing in stock you typically have a ...
0
votes
1answer
21 views

Loan Repayments and Yield Rates

Jose loans Martin $12000$. Martin repays the loan by paying $5000$ at the end of two years and $10000$ at the end of $4$ years. The money received at time $t=2$ is immediately reinvested at an annual ...
1
vote
2answers
174 views

Stochastic Calculus For Finance: Conditional Expectation of Binomial Tree Model

I'm reading through Stochastic Calculus For Finance Volume 1, page 32. The conditional expectation of $S_2$ knowing $1=H$ is $p*S_2(HH) + q*S_2(HT) = 0.5*16 + 0.5*4 = 10$ But how do I calculate the ...
0
votes
1answer
224 views

How to convert an interest rate from bank discount basis to continuous compounding

I read on Investopedia that a 360-day-count convention is being used in the case of Bank Discount Basis. And I found the following formula on Wikipedia: ...
1
vote
1answer
183 views

Calculating the yearly payment in a loan. Amortization with unequal payments.

The following is the problem that I am working on. A 30-yr loan of $1,000$ is repaid with payments at the end of each year. Each of the first ten payments equals the amount of interest due. Each ...
-2
votes
1answer
52 views

Differential of two geometric brownian motions

I am currently taking a finance course which includes some math that is currently above my level, it is however not a pure math class and we are just supposed to be able to apply the math to the given ...
0
votes
1answer
36 views

Calculating the loan from amortization.

I was not quite sure what the question was asking and I would like to have some input. a), Is it asking us to actually calculate knowing what each principal paid? or b), Working from almost complete ...
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
55 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
258 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
366 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
228 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
317 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
206 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
37 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
192 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
71 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
620 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
1k 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
117 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
41 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
284 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
121 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
136 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
67 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
130 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 ...