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

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Need help and clarification in Exam FM problem, future value.

The problem that I am working on is the following. Jim began saving money for this retirement by making monthly deposits of 200 into a fund earning 6% interest compounded monthly. The first ...
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7 views

After-Tax EAR given APR, and Tax Rate [on hold]

Consider an account that pays 6% APR(Quarterly). Assume the tax rate is 30%. Determine the after-tax EAR to the nearest .001% if taxes are paid semi-annually.
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The Present Worth of $169 due in 2 years at 4% Per Annum Compound Interest

The present worth of $\$169$ due in 2 years at $4\%$ per annum compound interest is The choices are as follow: $\$150.50$ $\$154.75$ $\$156.25$ $\$158$ I tried to solve this by multiplying $169$ ...
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1answer
18 views

Whats the formula to work out the minimum monthly payment of a loan?

I'm a developer, and i'm building a snowball debt calculator. I want a formula to work out what the minimum monthly repayment would be on a debt with a given interest. And I really want to get the ...
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2answers
14 views

FV (Future Value) of annual payments

My client will receive $\$881$ now and twice that amount in a year. He will get 3 times $\$881$ in 2 years . 4 x $\$881$ in 3 years etc. for as long as he lives. Assuming he lives 20 years and each ...
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0answers
12 views

local martingales and dividend processes

Consider a $d+1$ asset, continuous-time model where asset $0$ is a riskless numeraire. Assume that the asset prices are modelled by a $(d+1)-$dimensional Ito process (B,S). Further, let $D$ be the ...
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1answer
44 views

Exam FM problem. What does this problem mean?

Danny borrows 4,000 from Genevive at an annual effective rate of interest i. He agrees to pay back 4,000 after 14 years and 5,440.32 after another 14 years. Danny repays the ...
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2answers
16 views

Methods of solving this exam FM problem with geometric-investments.

The problem I am working on is as follows. Matthew makes a series of payments at the beginning of each year for $20$ years. The first payment is $100$. Each subsequent payment through the tenth ...
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41 views

Simple Interest question [closed]

Guy borrow $3150 from guy2 to pay tuition. He will repay in 6 months with interest at 4%. How much interest amount to? What amount must he pay at the end of 6 months?
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1answer
29 views

Pricing a riskless asset in the Black & Scholes market

Consider a Black&Scholes Market where a risky asset evolves according to: $$\frac{dS_t}{S_t}=\mu dt+\sigma dB_t$$ $$S_o=s$$ Riskless asset is associated with risk free rate r. I want to represent ...
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31 views

Can someone check my answers to this problem?

This is from Discrete Mathematics and its Applications Definition of recurrence relation from book From my understanding, compounded annually means that every year(annually) the account will ...
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1answer
35 views

Exam FM problem with loans. $(1.0075)^2$ or $(1.0075)^3$?

I am a bit confused about the following problem and I would like to have clarification. A loan of $12,000$ was made with annual rate of $12\%$ convertible quarterly. Smith plans to make a ...
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1answer
14 views

Calculating the yield of a bond purchased at a lower price.

I am working on the following problem. A 10 year bond bearing a $7\%$ coupon rate payable semiannually is bought to yield $5\%$ semiannually. The bond is redeemable at par. If the bond is ...
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1answer
14 views

Algebraic representation of how values are calculated in TI BA II+?

In order to understand how the BA II+ works, I would like to know the algebraic representation of it. For example, for the problem below Present value of an annual coupon bond that pays 80 per ...
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1answer
28 views

Exam FM problem. Bonds

the following problem is what I am working on. Suzan can buy a zero coupon bond that will pay $1000$ at the end of $12$ years and is currently selling for $624.60$. Instead she purchases a $6\%$ ...
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1answer
46 views

How do you compute such a limit? (Where the variable is the upper limit in a definite integral)

I have computed limits rigorously before but I have never come across an example where the variable is located in the upper limit of a definite integral. The exact question is attached. It's shown ...
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22 views

I have questionin from the stochastic differential equation merton model

in the following stochastic differential equation merton model we have $$\frac{ds}{s}=(\alpha-\lambda k)dt+\sigma dW+dq$$ where $\alpha$ is the instantaneous expected return on the stock; ...
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1answer
99 views

Heavy-tailed distributions

I have encountered the following two definitions of heavy-tailedness (right tail) for a $[0,\infty)$-valued random variable $X$ satisfying $\mathbb{E}[X]<\infty$: (i) ...
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2answers
60 views

Interest rates. What is the difference between $I=I_0(1+r)^t$ and $\frac{dI}{dt}=rI$?

When I was in school, we used this method for generating the amount of money would be in a bank account after $t$ years with interest rate $r$: $$I=I_0(1+r)^t \text{ where }I_0\text{ is the initial ...
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1answer
48 views

Conditional likelihood of continuously-combounded returns

The simplest possible asset pricing model ist the geometric brownian motion for asset price. Here the price $S_t$ solve the familar $$dS_t = (\mu +0.5 \sigma^2)S_t \, dt + \sigma S_t \, ...
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33 views

Find present value of employee given human capital investment

Here is the problem that I wanted to get a directions on: John Doe earns $80000$ a year. By 6th month of his employment company's HR determined that John needs human capital investment totaling ...
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1answer
21 views

Find compound growth rate from cumulative totals

I'm a bit out of my depth here, so please feel free to correct any errors in terminology, etc. I'm looking to solve for a percentage growth rate. I know the starting population, the number of ...
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1answer
33 views

How to calculate savings over the life of a car loan?

I'm working through the maths in this, only the relevant parts of which I quote: ...On a \$25,000 car loan through the manufacturer for four years, your monthly payment would be about [1.] \$520 ...
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0answers
52 views

Simplifying $\sum_{t=1}^{n}t^2v^t$ using actuarial notation.

In financial mathematics involving immunization, I encounter situations where I am trying to calculate $$(A) \quad v+4v^2+9v^3+ \cdots +n^2v^n=\sum_{t=1}^{n}t^2v^t $$ where $v$ is the present value ...
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Are these two option valuation formulas equivalent? Why?

I have been reading a finance paper that claims that the following function, which is a value for a financial derivative (1): $$V(s,t)=E_{Q} \left[\zeta\big(S(T)\big)e^{-\int_t^T r_F(\nu) ...
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1answer
36 views

Exam FM Portofolio problem: Using Macaulay Duration

The following problem is what I am working on and I cannot solve it. Under the current market conditions Bond 1 has a price (per 100 of face amount) of $P_1=88.35$ and a Macaulay duration of ...
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0answers
25 views

Macaulay duration for a coupon bond. Proof

I am working on showing the following. There is a coupon bond redeemable at par with annual coupon rate $r$ per year. The yield to maturity is $i$. The total number of coupons is $n$. Show ...
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1answer
18 views

Calculating interest on changing principal amount

I'm writing software and I'm trying to calculate interest on a principal value that changes daily in a predictable way. For example, if you saved $5 each day for five years at a 4% annual interest ...
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0answers
23 views

Calculate year for a provided yield

\$146.25 will yeild \$46.25 at 7.5% per annum. How to get the number of years? Answer is 6 but how do you get it? What is the formula?
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1answer
39 views

Advice inquiry: Financial mathematics

I am a math instructor at an education center studying to become an actuary. Currently I am studying for Exam FM and practicing problem from a book. Some of the problems in the book says "use a ...
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1answer
17 views

How to solve a Compound Interest Question with yearly withdrawals?

The current period is January 2015 A Principal wants to make 3 deposits in the bank: Start of 2015, Start of 2016, Start of 2017, And wants to give a $5000 scholorship for to the best student at ...
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24 views

A calculation for short term loans with different periods

I'm trying to come up with an equation that will allow me to calculate interest for short term loans. These are normally compounded monthly, however, they can be compounded weekly, and the periods ...
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33 views

Why doesn't this interest calculation add up

I'm trying to develop a calculation for returning the monthly payment for short term loans. Thanks to mardat, I've got an equation like this: 200=x*(1-(1+0.22)^-3)/0.22 = 97.93 Where 300 is the ...
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1answer
28 views

Find expected present value of a continuous payment stream

I have a question for the financial part of my course which I am struggling to answer as i am not sure my answer makes sense. Question: Time is counted from the present t = 0 in years. Suppose for ...
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39 views

Finding Joint Probability of a Binomial Tree Model given the stock price , then Conditional Probability

Consider a T-period binomial tree model with stock price $S_{t,n} = S_0u^nd^{t-n}$ at each node $(t,n)$ of the binomial tree for every $n = 0,1,...,t$ and every $t = 0,1,...,T$. a) Let $v,t \in ...
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1answer
31 views

Prove the process is a martingale with respect to the natural filtration

Let $\{M_n\}_{n\ge 0}$ be a symmetric simple random walk. Fix a real $b$. Prove that the process $S_n = e^{bM_n} (\frac{2}{e^b + e^{-b}})^n$, $n = 0,1,2,....$, is a martingale w.r.t. the natural ...
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1answer
31 views

How to differentiate the standard normal deviation w.r.t. a parameter inside the upper bound

Given that $$N(x)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^x e^{-\frac{s^2}{2}}\:ds$$ And that $$d=\frac{1}{\sigma\sqrt{\tau}}\ln\left({\frac{S}{e^{-r\tau}K}}\right)+\sigma\sqrt{\tau}$$ How do I take the ...
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1answer
63 views

How do I calculate interest on short term loan?

I'm trying to work out interest on short term loans - these are loans that extend to months not years, and are typically repaid in monthly chunks, but I also know that some are repayable in weekly ...
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1answer
29 views

How to differentiate the Black-Scholes formula w.r.t. volatility

The Black-Scholes-Merton formula for determining call option value is given as: $$C(S,K,\sigma,r,\tau)=N(d_1)S-N(d_2)Ke^{-rT}$$ where $N(d_i)$ is the standard normal distribution and ...
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1answer
33 views

Construct a strategy to profit: Problem involving term structure and interest rates.

I am currently studying about term structure and interest rates such as forward rates, swap rates, etc... The following problem seems like an actual actuarial problem that I might see in the future ...
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32 views

What is this sort of optimisation called?

I am reading a book in mathematical finance. There is something about constrained optimisation. They have specialised it for the financial market, but I am wondering what the general name for this ...
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1answer
26 views

Find the annual yield rate. Exam FM problem.

I'm trying to solve for the following problem and I cannot get the right #. You are given the spot rates at time $t=1,\ 2 \ \text{and} \ 3$ as $s_0(1)=.15,\ s_0(2)=.10,\ \text{and} \ s_0(3)=.05$ ...
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1answer
25 views

Forward rate example, switching the investment.

I need explanation regarding forward rates for the following specific example. A zero coupon with spot rate $s_0(1)=.08$ and $s_0(2)=.09$ are available. a), Smith borrows $1$ and is obliged ...
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3answers
76 views

How long an investment will take to compund to a target amount

A man with $\$20,000$ to invest decides to diversify his investments by placing $\$10,000$ in an account that earns $7.2\%$ compounded continuously and $\$10,000$ in an account that earns $8.4\%$ ...
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2answers
34 views

Calculating monthly compounded interest

To solve the problem How long does it take for an investment to double in value if it is invested at 8% compounded monthly? I figured like this: $$2P = P(1 + 0.08)^t$$ where $P$ is an ...
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Purchasing a unit on fund $X$ calculating the dollar weighted and the time weighted rate of return.

I am currently working on the following problem trying to figure out the rate of return. Fund $X$ has unit values which are $1.0$ on Jan 1 05, $0.8$ on Jul 1 05 and $1.0$ on Jan 1 06. A fund ...
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0answers
14 views

Payoff on Call Option

Mr Draper makes an investment: for $C$ pounds he buys a call option on $1$ share with strike price $K$ and expiration time $T$. He also deposits $K^{e−rT}$ pounds in a bank account where interest is ...
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1answer
12 views

Dollar weighted method vs. Time weighted method Problem. Exam FM

The following is the problem that I am working on and I am having trouble. On Jan 1 2005, an investment account is worth 100. On Apr 1 2005, the value has increased to 103 and 8 was withdrawn. ...
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14 views

Finite expectation of bank account with CIR interest rate model

The CIR interest rate model is $$dr_t=(\theta-ar_t)\,dt+\sigma\sqrt{r_t}\,dW_t\;.$$ The money account with this interest rate is $$e^{\int_0^tr_s\,ds}\;.$$ It is known that ...
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1answer
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Dollar weighted return. Formula or definition?

I was learning dollar-weighted return and I was a bit puzzled by the following and I would like to have some advice. I understand that it's basically the internal rate return, but using simple ...