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A comprehensive set of practice problems covering key concepts in time value of money, including geometric mean return, interest-on-interest, discounting, effective annual rate, compounding, and more. Each problem includes a detailed solution, allowing students to understand the underlying principles and apply them to real-world scenarios. Ideal for students studying finance, accounting, or economics, providing a valuable resource for reinforcing their understanding of these fundamental financial concepts.
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QUESTION 2: TYPES OF TRADES Match each of the following trades with the appropriate sentiment: Trade Sentiment Buy a call option Optimistic about a stock Buy a put option Pessimistic about a stock Buy a stock on margin Short sell a stock Answer: Buy call option โ Optimistic about a stock Buy a put option โ Pessimistic about a stock Buy a stock on margin โ Optimistic about a stock Short sell stock โ Pessimistic about a stock
QUESTION 3: ANNUAL RETURN Consider an investment that produces a return of 3.5% in the first year, - 2% for the next year, and 5% for the last two years.
QUESTION 5: ANNUAL RETURN Consider a stock that had a $20 per share price on January 1 st
. At the end of three months, the stock had a price of $21 per share. What is the effective annual return for this stock? Answer: Return over three months = $21 โ 20 $ = 0. 05 Annualized return = (1 + 0.05) 4
QUESTION 6:YIELDS ON MONEY MARKET SECURITIES A US Treasury security has a price of 99.75, and 31 days to maturity. What is this securityโs discount yield and investment yield? Answer: Discount yield = 100 โ 99. 75 100
360 31
Investment yield = 100 โ 99. 75
365 31
QUESTION 1: GEOMETRIC MEAN RETURN Suppose that you invest $10,000 in an investment that will grow in value 6% the first year, 7% the second year, and 8% the third year. What is the average annual rate of return on this investment? Answer: Future value = $10,000 (1+ 0.06)(1+0.07)(1+0.08) = $12,249. Return = (^3) $12, 249. 36 $10, 000. 00
Alternatively: 3
QUESTION 2: INTEREST-ON-INTEREST Suppose you deposit $1 million in an account that pays 5% interest, compounded daily. What is the interest-on-interest that you earn over a six-year period? Answer: Interest-on-interest = FVcompounding โ FVsimple interest Future value with compound interest = $1 1 +
QUESTION 4: DEFERRED ANNUITY An investment promised $1,000 per year, at the end of each of five years, but the cash flows do not begin until four years from today. If the discount rate is 5%, what is the value of this investment today? Answer: PV three years from today = $1, 000 1 โ 1
QUESTION 5: EFFECTIVE ANNUAL RATE What is the effective annual rate of interest if the nominal rate is 6% and interest is compounded weekly? Answer: Effective rate = 1 +
QUESTION 7: COMPOUNDING Suppose you invest $10,000 in a security that grows 5% the first year and 6% the second year. What is the value of this investment at the end of the second period? 16 Answer: PV = $10, r 1 = 5% r 2 = 6% FV = PV (1 + r 1 )(1+r 2 ) = $10,000 (1.05) (1.06) = $11,
QUESTION 8: DISCOUNTING Suppose you expect $10,000 in three years. The appropriate discount rate in the first year is 4%, the second is 5%, and the third is 6%. What is the present value of this cash flow today? Answer: FV = $10, r 1 = 4% r 2 = 5% r 3 = 6% PV = $10, 000 ( 1. 04 )( 1. 05 )( 1. 06 ) = $๐, ๐๐๐. ๐๐
QUESTION 10: DISCOUNTING WITH CONTINUOUS COMPOUNDED RATES Suppose you expect $1,000 in three years. If the discount rate is 8%, continuously compounded, what is the present value of this future cash flow? Answer: FV = $1, I = 8% PV = $1, 000 ๐
QUESTION 11:VALUATION WITH A GROWING PERPETUITY Suppose a stock pays annual dividends, and that todayโs dividend is $2 per share. If dividends are expected to grow at a rate of 5% per year, and the required rate of return on this stock is 8%, what is the value of this stock today? 20 Answer: D 0 = $ g = 5% r = 8% PV = ๐ท 0 ( 1 +๐) ๐ โ๐
$2 ( 1 + 0. 05 )