# Exercise on Tvm

Dr. Huiyan Qiu

TVM and No-Arbitrage Principle: practice questions and problems Work on the following problems to check your knowledge on the time value of money and no-arbitrage principle. 1. An interest rate is quoted as 5% per annum with semiannual compounding. What is the equivalent rate with (a) annual compounding, (b) monthly compounding, and (c) continuous compounding? 2. An investor receives $1,100 in one year in return for an investment of $1,000 now. Calculate the percentage return per annum with: (a) Annual Compounding, (b) Semiannual Compounding, (c) Monthly Compounding, and (d) Continuous Compounding. 3. Your grandfather put some money in an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money for the first time. The account currently has $3996 in it and pays an 8% effective annual interest rate. a. How much money would be in the account if you left the money there until your 25th birthday? 65th birthday? b. How much money did your grandfather originally put in the account? 4. Five years ago, you purchased 100 shares of stock which pays share dividend with continuous compounding rate of 1%. The current stock price is HK$50 per share. What is the value of your stock investment? 5. If you need €15,000 in three years, how much will you need to deposit today if you can earn 8 percent per year compounded continuously? 6. Suppose Bank One offers a risk-free interest rate of 5.5% on both savings and loans, and Bank Enn offers a risk-free interest rate of 6% on both savings and loans. The interest rates offered by the two banks have same compounding frequency. a. What arbitrage opportunity is available? b. Which bank would experience a surge in the demand for loans? Which bank would receive a surge in deposit? c. What would you expect to happen to the interest rates the two banks are offering? 7. Suppose the stock price is $35 and the continuously compounded interest rate...

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