The Mathematics of Money

(Darren Dugan) #1

300 Chapter 6 Investments



  1. The Hopewell Asian Markets Telecommunications Fund is a closed-end fund. There are 2,814,000 shares outstanding,
    and the fund’s total assets are $89,035,047. Shelly bought 100 shares of this fund. How much did she pay for them?


D. Measuring Fund Performance



  1. Mehmet invested $4,000 in an open-end, no-load mutual fund when the NAV was $34.35 per share. He has reinvested
    all dividend and capital gains distributions. Five years later, his account statement showed that he owned 124.570
    shares, and the NAV had grown to $57.02. Determine:


a. The total profi t Mehmet has earned on this mutual fund.
b. The average annual rate of return (CAGR) on this investment.


  1. Louise invested $5,000 in an open-end, no-load mutual fund. The NAV was $14.47. All distributions have been
    reinvested. Three years later, she owns 472.516 shares. The NAV is $14.45. What is the CAGR she has earned on this
    investment?

  2. I invested $3,257.09 in an open-end mutual fund with a 3.5% load. The NAV was $59.95. All distributions were
    reinvested. Seven years later, I owned 72.58 shares with an NAV of $52.08. What CAGR did I earn on my investment?

  3. The Hopewell Aggressive Growth Fund has achieved returns of 47.5%, 32.1%, 11.3%, 9.2% and 13.2% in the
    last 5 years. What is the average rate of return over this period?

  4. The Hopewell U.S. Government Bond Fund had returns of 20%, 8%, and 12% in the last 3 years. If I invested in
    this fund 3 years ago, is the value of my investment more than, less than, or the same as it was 3 years ago? What is
    the average rate of return over this period?


E. Grab Bag



  1. Find the NAV of a mutual fund portfolio if the total assets are $103,569,101 and the number of shares is 8,504,219.

  2. True or false:


a. Investing in a diversifi ed portfolio guarantees that you will not lose money in any given month.
b. Investing in a diversifi ed portfolio guarantees that you will not lose money in the long run.
c. Investing in a diversifi ed portfolio guarantees that you will not do as well as if you had invested all your money in
the best stock from the portfolio.
d. Investing in a diversifi ed portfolio guarantees that you will not do as badly as if you had invested all your money in
the worst stock from the portfolio.
e. The growth of a diversifi ed portfolio will be as smooth as it would be with a constant rate of compound interest.


  1. Rick’s investment advisor has told him that he should invest 70% in stocks, 25% in bonds, and 5% in cash. Using the
    values given in the table, determine a reasonable rate that he might expect this portfolio to return, using (a) the low-end
    rates and (b) the high-end rates.

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