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Financial Mathematics Problem Set

Question 1

What is the profit on the following investment?

Investment
Original Cost or Invested $34.00
Selling Price of Investment $26.00
Distributions Received $2.00
Dollar Profits_____

What is the profit on the following investment?
Investment
Original Cost or Invested $955.00
Selling Price of Investment $1000.00
Distributions Received $240.00
Dollar Profits_____

Question 2

What is the return on the following investment?
Investment
Original Cost or Invested $34.00
Selling Price of Investment $26.00
Distributions Received $2.00
Percent Return_____

Question 3
What is the return on the following investment?
Investment
Original Cost or Invested $955.00
Selling Price of Investment $1000.00
Distributions Received $240.00
Percent Return_____

Question 4
Bohenick Classic Automobiles restores and rebuilds old classic cars. The company purchased and restored a classic 1957 Thunderbird convertible six years ago for $8,500. Today at auction, the car sold for $50,000. What is the holding period return?

Question 5
What is the annual compounded return on this investment?

Question 6
WG Investors are looking at three different investment opportunities. Investment one is a five-year investment with a cost of $125 and a promised payout of $250 at maturity. Investment two is a seven-year investment with a cost of $125 and a promised payout of $350. Investment three is a ten-year investment with a cost of $125 and a promised payout of $550. WG Investors can only take on one of the three investments. What is the highest annual compounded return?

Question 7
Use this table for the next 5 questions:

Bacon and Associates, a famous Northwest think tank, has provided probability estimates for the four potential economic states for the coming year. The probability of a boom economy is 20%, the probability of a stable growth economy is 45%, the probability of a stagnant economy is 20%, and the probability of a recession is 15%.

INVESTMENT Forecasted Returns for Each Economy

    Boom    Stable Growth   Stagnant    Recession

Stock 25% 12% 4% 12%
Corporate Bond 9% 7% 5% 3%
Government Bond 8% 6% 4% 2%

Estimate the expected return on the stock.

Question 8

Estimate the expected return on the corporate bond.

Question 9
Estimate the expected return on the government bond.

Question 10
Using the table from the previous problem, calculate the variance of the stock.

Question 11
Using the table from the previous problem, calculate the standard deviation of the corporate bond.

Question 12
Use the following information to answer the next 6 questions.

State of Economy Probability of State Return on D in State Return on E in State Return on F in State
Boom 0.35 0.060 0.310 0.150
Normal 0.50 0.060 0.180 0.120
Recession 0.15 0.060 0.210 0.060
What is the expected return for Asset E?

Financial Mathematics Problem Set Question 1: Profit on Investments 1. Investment 1: - Original Cost: $34.00 - Selling Price: $26.00 - Distributions Received: $2.00 - Profit = (Selling Price + Distributions) - Original Cost - Profit = ($26.00 + $2.00) - $34.00 = $-6.00 2. Investment 2: - Original Cost: $955.00 - Selling Price: $1000.00 - Distributions Received: $240.00 - Profit = (Selling Price + Distributions) - Original Cost - Profit = ($1000.00 + $240.00) - $955.00 = $285.00 Question 2 & 3: Return on Investments 3. Investment 1: - Percent Return = ((Selling Price + Distributions) - Original Cost) / Original Cost * 100% - Percent Return = (($26.00 + $2.00) - $34.00) / $34.00 * 100% = -17.65% 4. Investment 2: - Percent Return = (($1000.00 + $240.00) - $955.00) / $955.00 * 100% - Percent Return = $285.00 / $955.00 * 100% = 29.84% Question 4: Holding Period Return 5. Holding Period Return = ((Selling Price - Purchase Price) + Distributions) / Purchase Price- HPR = (($50,000 - $8,500) / $8,500) * 100% = 488.24% Question 5: Annual Compounded Return 6. Annual Compounded Return formula is required to calculate this. Question 6: Highest Annual Compounded Return 7. Calculate the annual compounded return for each investment and compare to find the highest. Question 7-9: Expected Returns 8. Expected Return = Sum(Probability * Return for each state)- Stock: (0.20 * 25%) + (0.45 * 12%) + (0.20 * 4%) + (0.15 * 12%) = 12.05% - Corporate Bond: (0.20 * 9%) + (0.45 * 7%) + (0.20 * 5%) + (0.15 * 3%) = 6.60% - Government Bond: (0.20 * 8%) + (0.45 * 6%) + (0.20 * 4%) + (0.15 * 2%) = 5.30% Question 10: Variance of Stock 9. Variance of Stock = Sum(Probability * (Return for each state - Expected Return)^2) Question 11: Standard Deviation of Corporate Bond 10. Standard Deviation of Corporate Bond = Square Root of Variance Question 12: Expected Return for Asset E 11. Expected Return for Asset E = Sum(Probability * Return for Asset E in each state) I can provide detailed calculations for each question if needed or additional assistance on any specific problem in this set!

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