Financial Mathematics Exam - Exámenes de Matemática Financiera

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FINANCIALMATHEMATICSSAMPLE

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Surname......................................................………..................................

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EXAM RULES

 Pleasewriteyouranswersinsidetheboxes.

 Donotusepencil.

 Onlythestapledexamwillbehandedin.

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FIRSTPART:

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1.Defineandexplaintheconceptof“financialtransaction”.

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2.Obtaintheannualnominalinterestratepayablemonthlyandthemonthlyeffectiveinterestratewhich

areequivalenttoa4.55%annualeffectiverate.

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3.SettheequationthatwouldallowyoutoobtaintheamountXsothatthetwofollowingcashflowsetsare

equivalentusingthecompoundinterestruleandaconstantinterestratei.

OF:{(C0,0),(C4,4)}

IF:{(C´1,1),(C´5,5),(C´7,7),(X,9)}

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4.Aninvestorbuys,throughabroker,afinancialassetthatgivestherighttoreceiveanominalamountof

5,000Eurosafter180days.Thepricepaidforthisassetiscalculatedwiththesimpleinterestrule,usinga5%

annualinterestrate.Theinvestormustpaytothebrokerabrokeragefeeof0.30%ontheasset’snominal,at

thepurchasedate.Calculatethetrueeffectiverateofreturnfortheinvestor.

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5.AssumethatapersondepositsanamountV0the10thofFebruary2009inordertoreceiveanannual

constantannuityof1,000eurosduring15years,startingthefollowingyear.Thisis,thefirstamountofthe

annuitywouldbereceivedthe10thofFebruary2010.A3%annualeffectiverateisusedduringthefirstfive

yearsanda4.5%annualeffectiverateisusedduringthelasttenyears.ObtaintheamountV0thatshouldbe

deposited.

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FINANCIAL MATHEMATICS SAMPLE

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EXAM RULES

 Please write your answers inside the boxes.  Do not use pencil.  Only the stapled exam will be handed in.

FIRST PART:

Define and explain the concept of “financial transaction”.
Obtain the annual nominal interest rate payable monthly and the monthly effective interest rate which are equivalent to a 4.55% annual effective rate.
Set the equation that would allow you to obtain the amount X so that the two following cashflow sets are equivalent using the compound interest rule and a constant interest rate i. OF: {(C 0 , 0), (C 4 ,4)} IF: {(C´ 1 ,1), (C´ 5 ,5), (C´ 7 ,7), ( X ,9)}
An investor buys, through a broker, a financial asset that gives the right to receive a nominal amount of 5,000 Euros after 180 days. The price paid for this asset is calculated with the simple interest rule, using a 5% annual interest rate. The investor must pay to the broker a brokerage fee of 0.30% on the asset’s nominal, at the purchase date. Calculate the true effective rate of return for the investor.
Assume that a person deposits an amount V 0 the 10 th^ of February 2009 in order to receive an annual constant annuity of 1,000 euros during 15 years, starting the following year. This is, the first amount of the annuity would be received the 10 th^ of February 2010. A 3% annual effective rate is used during the first five years and a 4.5% annual effective rate is used during the last ten years. Obtain the amount V 0 that should be deposited.

Obtain the expression for the Interest (I) when the compound interest rule is used and an amount C is invested during n years at an annual interest rate i.
Assume that you ask for a €90,000 loan with monthly constant instalments, 3% nominal interest rate and five years length. Calculate the constant periodic payments, and the interest payment and principal repayment corresponding to the first payment.
Represent graphically on a time line the following annuity whose financial value at time τ is given by: ܸ ఛ ൌ 200ܽ (^) ହഥ|௜ ሺ1 ൅݅ ሻ ଵ/ସ Assume that ݅ stands for an annual effective rate and that the first amount is paid the 1 st^ of February 2015. Indicate also the exact date for τ.
Explain the difference between a positive outstanding balance and a negative outstanding balance.
What would be the price paid (market value) the 1 st^ of October 2014 for a bond with annual coupons at 3% annual effective rate and nominal value of 1,000 Euros, issued the 1 st^ of April 2013 and with maturity date 1 st^ of April 2016, if the (annual effective) market interest rate on the purchase date was 2%?
Prove, mathematically, step by step, the decomposition of the total periodic payment (a (^) s) of a loan into

interest payment (Is ) and principal repayment (As ). In order to do so, you will have to use the outstanding balance calculated using the recursive method.

In order to obtain the 21 st^ of January 2016 an accumulated value of €40,000, a person signed the following savings plan with a bank: to make eight annual payments that would be constant during the first five years and also constant but double the amount the remaining years. Taking into account that the first payment was made the 21 st^ of January 2008 and that the bank paid a 2.75% effective rate the first two years and a 1.5% the six remaining years, obtain the payments made by this person each one of the years.

Financial Mathematics Exam, Exámenes de Matemática Financiera

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FINANCIAL MATHEMATICS SAMPLE

Group………………….

Surname......................................................………..................................

Name....................................

EXAM RULES