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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Suppose you invest \$10 at 10.2% per annum compounded annually. How many years would it take for your investment to grow to \$15 000?

I'am solving a simlar equation to this and just trying to figure out how they did it? the only part I don't understand is how they got the number.... 1.102 15000 = 10(1.102)n ¬1 mark 1500 = 1.102n
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1answer
69 views

first order differential question

Mr. John want to buy a house and he must borrow $150,000 from the bank. He wants a 30-year mortgage and he has 2 choice. Choice #1, he can borrow money at 7% per year with no point ( each point is ...
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2answers
119 views

Probability related finance question: Need a more formal solution

You are offered a contract on a piece of land which is worth $1,000,000$ USD $70\%$ of the time, $500,000$ USD $20\%$ percent of the time, and $150,000$ USD $10\%$ of the time. We're trying to max ...
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0answers
17 views

What is a rolling par-swap?

I am trying to understand the hedging strategy mentioned in the paper below on p.17 (set of rolling par-swaps). Can anyone explain how this works? Moreover, if anyone is familiar with this paper, ...
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1answer
38 views

Can anyone show me how this was derived?

So here is all the slide says and I'm and trying to see the steps for derivation. Can someone please show me how this is derived? Essentially I'm trying to go from 1 to 2. Pi is the profit function. ...
4
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1answer
93 views

Calculating interest rate for a payment plan

I really should know this from high school so I'm a bit ashamed to ask... :) I've been offered several cars for lease and want to compare the offered interest rates. E.g. I have: ...
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0answers
40 views

Programming in R: How do I switch the X and Y axes?

I have a distribution plot of the daily drawdowns of the Dow Jones Industrial Average index; however, it has the drawdowns on the y-axis and the frequency on the x-axis... I'd like to switch that so ...
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5answers
232 views

Game Theory Question about Financial Markets

This is a recent quote from one of the outstanding bond portfolio managers: "First of all, for every buyer there is a seller. Therefore, in order for someone to sell their bonds and buy stocks means ...
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1answer
53 views

Find the transaction cost-adjusted expected return of the stock

Let $W^b_i$ denote the weight of stock i in the existing portfolio and $W^a_i$ denote the weight of stock i in the new portfolio to be created. Let $c_i$ denote the transaction cost of stock $i$. If ...
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0answers
34 views

Stochastic control, numerical, need expectations given coupled SDEs

I'm looking at a trio of processes which arises in a stochastic control situation. I have a process $(V_t)$ which I may control, and $(V_t)$ influences a diffusive stock price process $(S_t)$. The ...
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3answers
90 views

If you invest $\$1500$ at $7\%$ compounded annually, how many years would it take for your investment to grow

If you invest $\$1500$ at $7\%$ compounded annually, how many years would it take for your investment to grow to $3750$? Is this right? $$\text{term } = \frac{\log( \text{overall gain factor})}{ ...
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1answer
74 views

confusing part to basic accounting question

Directions: Given the information find the weekly and monthly taxable wages (4.3 weeks per month). This is for federal income taxes. Weekly Taxable Wages: $\$21.40$ per hour, $40$ hours a week, $47$ ...
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0answers
80 views

determine the effective annual yield rate

The American Savings Bond of 1958 were 15 year bonds sold and redeemable at par with annual coupons, the first at 3.5% and the remainder at 4.25%. If the bond is help to maturity, determine the ...
0
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1answer
51 views

How to Maximise Efficiency With hp12c gold calculator: Equation of Value Loan Schedule

I would like to calculate the net present value of a loan schedule or an equation of value. e.g. "For an investor receives R1 000 after 2 years, R2 000 after 5 years and R4000 after 7 years, how much ...
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1answer
95 views

Binomial expansion for solving american put option identity [duplicate]

For american put option I have to prove that: 1) As $D$ tends to $\infty$, $a_n$ tends to $-r/D$ so that $S^*$ tends to $0$. 2) As $D$ tends to $-\infty$, $a_n$ tends to $2D/ \sigma^2$ so that ...
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1answer
128 views

american put option

For a perpetual american put option $v(s)$, satisfies the following problem: $$\frac12\sigma^2S^2\frac{\mathrm d^2V}{\mathrm dS^2}+(r-D)S\frac{\mathrm dV}{\mathrm dS} - rV = 0\quad\text{for ...
2
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1answer
46 views

Financial Bonds 500 $1,000 bonds with stated rate of 5% issued at par. 10 year term and pay interest semi-annually.

Every time I try and calculate this problem something comes up wrong. Either from working it out by hand or using my BA II plus, I cannot get the answer shown below. Am I wrong or is this book answer ...
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2answers
23 views

In this situation, how to decrease the payout amount based on the “weighed” constituent parts?

Couldn't think of a better way to explain it in the title, my bad. This is a problem I'm running into in a programming project. Here's the situation: Say a partner is due to be paid $1000 for ...
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1answer
30 views

How to find breakeven amount when the buy and sell amount has a fee?

With currency exchange they charge 3% when I buy a currency. When I sell they charge 3% on the amount I sell. My question: At which amount do I need to sell to make up for the 3% fees? I currently ...
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0answers
38 views

Non-arbitrage theory and existence of a risk premium

Consider a probability filtred space $(\Omega, \mathcal F, \mathbb F, \mathbb P)$, where $\mathbb F = (\mathcal F_t)_{0\leq t\leq T}$ satisfing the habitual conditions and isgenerated by $1 d $- ...
2
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1answer
174 views

Bonds and Force of Interest

Studying for FM/2 and ran into this problem dealing with bonds; A 1,000 par value 3 year bond with annual coupons of 50 for the first year, 70 for the second year, and 90 for the third year is bought ...
2
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1answer
35 views

Calculating percentage reduction from results only.

I've been looking over some loan repayment statements, and I'm trying to work out: What the precentage interest is per month. How long it will be until the final amount reaches 0. Whether there is ...
0
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1answer
103 views

Find the price to yield 10% compounded semi-annually.

A 50,000 par value bond at 8% has semi-annual coupons and is callable at end of 12th through 15th years at par. Find the price to yield 10% compounded semi-annually.
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67 views

Calculate the time after which Money doubles

I while solving a problem in banking just thought to form a formula for the time period after which money deposited in bank at a compounded interest rate @$\alpha $ % p.a. . Amount for compounded ...
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1answer
997 views

Increasing and decreasing annuity

Going in circles..... Find an expression for the present value of an annuity-immediate where payments start at 1, increase by 1 each period up to a payment of $n$, and then decrease by 1 each period ...
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1answer
118 views

Continuous annuity calculation

This is a problem from Marcel Finan's Exam FM/2 course. It is not homework but I am studying for the FM exam and trying to get through this. You are given $\frac{d}{dt}\bar{s}_t$ = $(1.02)^{2t}$. ...
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1answer
120 views

Random Stock Stop-Loss/Stop

Assuming a Stock's price changes in a random manner. If you buy this Stock, you are required to set a stop-return and stop-loss price. I am looking for the equation that shows the probability for ...
0
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1answer
42 views

Bond worth given yield to maturity

On 18 February 2010, the bonds were issued with a face value of $1,000. The bonds mature in 15 April 2015 and have an annual coupon rate of 6%. (a) Assuming today is 15 April 2013, how much is the ...
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1answer
151 views

A loan is being repaid by 12 annual payments of 3000…determine the principal and interest portions of the tenth payment

A loan is being repaid by 12 annual payments of 3000 followed by 8 annual payments of 5000. If i=0.10, determine the principal and interest portions of the tenth payment and the 15th payment. I am ...
2
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2answers
137 views

Are there constraint problem calculators?

So I just remembered Lincoln Logs exist, so I found ten giant sets of them on ebay for Buy It Now, and I'm trying to decide what combination of purchases gives me the most logs for the least money if ...
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2answers
148 views

Calculating the same exchange rate to make an investor indifferent

If we consider an American investor in 2009 with 160 million Dollars to place in a bank deposit in either America or the UK. The (1 yr) interest rate on bank deposits is 6 percent in the UK and 1 ...
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1answer
121 views

Find the present value of a ten-year annuity

Find the present value of a ten-year annuity which pays $400$ at the beginning of each quarter for the first $5$ years, increasing to $\$600$ per quarter thereafter. The annual effective rate of ...
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3answers
6k views

Most efficient method for converting flat rate interest to APR.

A while ago, a rather sneaky car salesman tried to sell me a car financing deal, advertising an 'incredibly low' annual interest rate of 1.5%. What he later revealed that this was the 'flat rate' ...
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1answer
121 views

Find the accumulated value of an investment fund

Find the accumulated value at the end of six years of an investment fund in which \$100 is deposited at the beginning of each quarter for the first three years and \$50 is deposited at the beginning ...
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1answer
23 views

Find the relative shares of B,C and D in the estate, if it is assumed that the estate will earn a 7% annual eff

Person A leaves an estate of $100,000. Interest on the estate is paid at the end of the year to beneficiary B for the first 10 years, to beneficiary C for the next 10 years, and to charity D ...
2
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1answer
144 views

Is the following a martingale?

Let $X_{n}$ be a martingale with respect to a filtration $\mathbb{P}_{n}$. Define: $Y_{n}$ := $X_{n}^{3}$ Is $Y_{n}$ a martingale? Supermartingale?
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0answers
63 views

Doob Decomposition of American Option

I am trying to figure out the Doob decomposition of an American put option in a discrete time binomial model. I know how to price the American put, but I'm having trouble expressing it as the sum of ...
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3answers
89 views

A fund of $30,000 is used to award scholarships…If i=0.09, find the number of scholarships which can be awarded

A fund of $30,000 is used to award scholarships of amount 3000, one per year, at the end of each year for as long as possible. If i=0.09, find the number of scholarships which can be awarded and the ...
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2answers
54 views

If $ i=0.09 $, find $ n $ and the amount of final payment.

A fund of $ \$500 $ is to be accumulated by $ n $ annual payments of $ \$100 $, plus a final payment as small as possible made one year after the last regular payment. If $ i = 0.09 $, find $ n $ and ...
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2answers
153 views

at a nominal rate of interest of 8% converted semiannually…Find the initial amount of the loan.

A loan is to be repaid with level instalments payable at the end of each half-year for $3$ and $\frac{1}{2}$ years, at a nominal rate of interest of 8% converted semiannually. After the $4^{\rm th}$ ...
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1answer
388 views

Determine the effective annual interest rate on the loan

A borrower owes \$5000 today and has promised to pay \$1900 at the end of the next three years to repay the loan. Determine the effective annual interest rate on the loan. What is the outstanding ...
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2answers
137 views

Determine the monthly payments if the nominal rate is 12% converted monthly

a) A $\$50,000$ mortgage is to be repaid by monthly payments for $20$ years. Determine the monthly payments if the nominal rate is $12\%$ converted monthly b) an extra payment of $\$1,000$ is made at ...
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2answers
137 views

Why does the internal rate of return have no analytic expression?

I know that the IRR can be computed using iterative methods, but why is this necessary? What makes it impossible to give an expression for IRR? How would you prove it to be impossible?
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2answers
209 views

Profit and Loss calculation: Fake currency

A store buys an item for $\$50$. They price it then, at $\$80$ ($\$30$ profit margin). A customer buys the item from them with a fake $\$100$ note. The store returns $\$20$ to the customer. My ...
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1answer
2k views

How to convert interest rate to discount factor

I'm studying on Kellison's Theory of Interest and I'm stuck on the exercise 20/a of the 1st chapter. If the $i=0.1$ then $d = 0.0901$ $d_5=\frac{A_5-A_4}{A_5}$ when I insert $d$ into this ...
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1answer
95 views

Trouble arranging for interest in annuity to present value formula

The formula is: $$A = P\frac{i(i+1)^{n}}{(i + 1)^{n}- 1}$$ and I need to rearrange for $i$ because I don't know the interest. I can solve this if it were Any help would be greatly appreciated.
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2answers
65 views

Value of Investment in the Past

An amount of $1000$ is to be accumulated at a compound rate of discount of $9$% per year. (a) Find the present value $3$ years before (b) Find the value of i corresponding to d. For a) i have done ...
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2answers
192 views

Determine the simple interest rate under which a sum of money will double in 5 years.

Determine the simple interest rate under which a sum of money will double in 5 years. IS my following solution correct below? $A = p(1+r)^{t}$ $A/p = 2 =(1+r)^{5}$ $ln2 = 5ln(1+r)$ $ln2/5 = ...
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2answers
58 views

Cost for hedges under a Wiener process

I'm trying to estimate the hedging costs relating to a financial derivative which moves like a Wiener process, and I'm struggling to find the correct setup to solve the problem. Suppose I have a ...
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1answer
64 views

European Calls: arbitrage

I have following question, it should be pretty easy, but this subject is still pretty new for me. Given a market where calls of any strike price can be bought and sold. Assume that the interest rate ...