Homework on Savings accounts, Savings plans and Investments

  1. You deposit $4000 into a savings account that bears 5.1% interest compounded monthly. How much is the accumulation after 5 years?
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  2. There are three banks A, B and C in town. They all have an APR of 5%. Deposits in Bank A compound quarterly, in bank B it's monthly and in Bank C it's continuously. You deposit 100$ into each of them. What is the accumulation in each after 1 year?
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  3. There are three banks A, B and C in town. Which bank has the highest APY if:
    1. Bank A offers an APR of 4.75% compounded daily,
    2. Bank B offers an APR of 4.8% compounded monthly and
    3. Bank C advertises an APY of 4.81%.
       
  4. At the birth of his daughter, Jordan wants to set up a savings account with a deposit of $15,000. There are several  possibilities. Compute the accumulation of each of them after 18 years.
      1. account B returns 5.15% compounding quarterly
      2. account D returns 5.07% compounding continually
       
  5. You invest 1000$ over 10 years in a saving account compunding monthly. In a spreadsheet, compute the accumulation if the APR is one of the following percentages: 2, 2.1, 2.2, 2.3, ...., 3, 3.1, 3.2, ..., 4, 4.1, 4.2, ... 5, 5.1, 5.2, .....6. So in the A column, you put the percentage in decimal form: 0.02, 0.021 etc. In the B column you compute the accumulation based on the interest rate in the A column.
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  6. Manuela would like to take a trip to Africa in two years, which costs $8,000. Her bank offers her an APR of  5.6%, compounded monthly, for a certificate of deposit account. How much does she have to deposit right now, to achieve her goal?

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  7. At age 30, Michelle starts an IRA to save for retirement. She deposits $300 at the end of each month. Suppose the APR is  6.3%, compounded monthly.  How much will she have when she retires  35 years later at age 65? Compare the IRA's value to her total depositsover this time period.
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  8. You would like to retire  30 years from now, and you would like to have a retirement fund from which you can draw an income of 30,000 per year - forever. (Treat the 30,000 as simple interest on the amount A, that you have accumulated by that point). Suppose the APR is 8%, compounded monthly. How much would have to be in that fund? How much would you have to deposit each month to achieve that accumulation?
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  9. You invest $6,000 in the ABC mutual fund. Over 4 years, your investment grows in value to $9,800. What are your total and annual returns?
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  10. You purchased shares in Internet.com for $5,000. Three years later, you sold them for $3,700. What were your total and annual returns?
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  11. Suppose your great-grandmother invested $100 at the beginning of 1926 in each of the following: small company stocks (average annual growth rate: 12.6%), large company stocks (10.4), longterm corporate bonds (5.9%), and US Treasury bills (3.7%). Assuming her investments grew at the given rates, how much was each investment worthat the end of 2009?
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  12. The closing price of of a US Treasury bond with a face value of $1000 is quoted as 106.25 points (meaning it will now sell for 106.25% of the original price) , for a current yield of 5.2%. If you buy this bond how much annual interest will you receive?
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  13. On January 1st you have invested in three funds: stocks, bonds and raw materials and you track the share prices:
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    Date Stocks Bonds raw materials
    1/1 20 30 33
    2/1 23 28 32
    3/1 25 31 29
    Suppose your initial investment was 500$ in Stocks, 300$ in bonds and 200$ in raw materials. What is the value of your portfolio on 2/1 and 3/1?
       
  14. Given the mutual fund table in the notes and suppose that you invested $500 in the Social Investment Fund 3 years ago, what is your investment worth now? (Dividends  and gains are all reinvested.)
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  15. You would like to retire in 30 years with an annual income of  $20,000 in today's dollars (present value). Assume an average annual inflation rate of 2.5%.
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    What dollar amount would that correspond to in "30 years from now"-dollars?
    If this amount corresponds to 5% of a nest egg, how big is the nest egg?
    How much do you have to contribute monthly to reach it, supposing an APR of 5%?
       
  16. In 1997, your parents bought a house for $190,000. In 2007, they want to sell it. Use the CPI table, to estimate what that houseprice means in 2007 in inflation adjusted dollars.
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  17. What is the present value of a fortune of $1,000,000 in 25 years, if in the mean time there is annual inflation of on average 3.1%?
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  18. Suppose, next year your boss will give you a raise of 10%. At the same time inflation is 15%. What is your real gain/loss?
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  19. You have put $30,000 in an investment vehicle that returns 5.7% annually. However inflation runs at 3.1% annually. What is the present value of this investment in 10 years? What is the real growth of the investment over 10 years?