Financial Exercises 1: Discounting and compounding

by Clemens Werkmeister

1. Compounding and Discounting

a. If the present value of 400 € to be paid at the end of one year is 350 €, what are the one-year discount factor and the corresponding discount rate?
b. If the annual interest rate is 10 %, what are the discount factors for two years?
c. You invest 1.000 € at an annual interest rate of 6 %. What is the final value of the investment after 3 years, after 5 years, after 10 years?
d. Your bank offers you to invest 880 € in a certificate of deposit that promises a payment of 1.000 € after two years. What is the effective annual rate (EAR) of this certificate?
e. Your bank offers you a certificate of deposit that promises a payment of 1.000 € after two years. How much should you pay for that certificate, if the annual interest rate is supposed to be 7 % and there are no interest payments in the meantime (i.e. the certificate is a zero bond).
f. After how many years an investment doubles its value, if interest payments are reinvested at the interest rate of 10 %.
g. A zero-bond pays 1.000 € at the end of year 2014. Calculate the price of the bond at 30.06.2012, assuming an yield of 6 % for similar bonds?

2. Simple rate and effective annual rate

What is the value of an investment after one year (respectively the effective annual rate), if interest is paid
a. annually at 12 %,
b. quarterly at 3 %,
c. monthly at 1 %,
d. daily (at 360 days) at 12 / 360 %,
e. continuously at a rate of 12 %?

3. Continuous compounding

What is the continuously compounded return (force of interest) corresponding to an annual rate of 6 %?

4. Value of a cash discount

An invoice with a regular 30-day-payment-term allows you a cash discount of 3 % for paying within ten days. Should you accept the discount?

5. Forms of payment

You want to buy a car with a list price of 30.000 €. The car seller offers you the following payment schedules:

• You pay a cash down payment of 10.000 € and three rates of 7,000 € each at the end of years 1, 2, and 3.
  
• You pay cash with a discount of 3 %.
  

a. Which one is the better schedule if you own 40.000 €, invested at 5 %?
b. What cash discount is necessary to make cash payment the better alternative?

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References:
- NPV
- Financial Resources Formulary
- Financial Exercises