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A financial mathematics exam from july 2012, which covers topics such as accumulation of annuities, cash flow streams, annuity value arrangements, statements about investment returns, and bond issues. It includes 6 questions with sub-parts, providing a comprehensive assessment of the student's understanding of financial mathematics.
Tipo: Ejercicios
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Departamento de Economía Financiera y Actuarial
35883 - MATEMATICAS FINANCIERAS / FINANCIAL MATHS EXAM SESSION: JULY 2012 SURNAME: NAME: GROUP: AR
Please write your answers inside the boxes.
Prove that the accumulation of an immediate annuity-certain, S (^) n | i , is equal to i
( 1 i ) n^ 1 , being i
the effective interest rate per period.
Consider a financial transaction defined by the following cash-flow streams:
Cash outflows: C 0 C 4 C 6 C 7
Cash inflows: C’ 1 C’ 3 C’ 8
0 1 2 3 4 5 6 7 8
Money is valued at a compound interest rate per period i. Find:
2.1) The equation of value at time t = 3.
2.2) The outstanding balance at time t = 4 after the cash flow C 4. Use the retrospective method.
2.3) The outstanding balance at time t = 7 before the cash flow C 7. Use the recursive method , based on the outstanding balance computed at t = 4.
2.4) Consider that C 0 = (C’ 1 + C’ 3 ). In such a case, can the original lender become the debtor at some time? Explain your answer.
4.2) The outstanding balance in a zero-coupon bond is always the face value of the bond.
4.3) In an adjustable-rate loan with predetermined instalments, the true effective rate of financing cost for the borrower can be computed at the beginning of the financial transaction, since the amounts of the periodic payments are known from the very beginning.
4.4) At simple interest, it is necessary to double the annual interest rate in order to double the interest earned when C monetary units are invested for n years, if n > 1. At compound interest, however, it is not necessary to double the annual interest rate in order to double the interest earned by investing the same amount for the same period of time.
Mr. Smith wanted to accumulate EUR50,000 by the end of 10 years. His bank suggested him three possibilities to carry out the financial transaction:
a) Constant monthly payments. b) Monthly payments increasing 0.5% each month. c) Monthly payments constant during the year and increasing 5% each year.
In all cases the annual nominal interest rates payable monthly used by the bank are 3% for the first 3 years and 3.60% for the remaining 7 years. Moreover, the first deposit should be made 09.07.12, so the accumulated EUR50,000 will be available on 09.07.22.
Use the available information to obtain the amount of the first and last deposits to be made on 09.07.12 and 09.06.22, respectively, for the three alternatives detailed above.
First possibility
Second possibility
Third possibility
a. Find the instalments for the first two years to be paid to Bank A. Suppose that the index rate for the second year is 3.45%.
b. Components (interest payment and principal repayment) of the instalment due on May 9th,
c. Find the amount to be paid to cancel off the original loan with Bank A on February 9th,
d. Find the instalment due today, 9th^ of July 2012, of the new loan with Bank B. Assume that the principal of the new loan is of the amount needed to prepay the first loan.
e. Set the equation that would allow you to find out the borrowing true effective rate of the joint financing transaction. Suppose that €2,500 is the total amount of expenses to be paid at the new loan settlement date (the loan origination fee is included in that amount).
a) Total amount received by Mr. Pérez for selling 100 bonds on 15.07.
b) Set up the equation of value to obtain the effective rate of return earned by Mr. Pérez from his investment in the bonds. Would this effective rate of return be higher or lower than the coupon rate (5%)? Why?
