Question

1. In five years your oldest child will be in 8th grade, at which point you and your family plan to vacation in Europe. You estimate that you will need $20,000 for the trip. How much do you need to set aside today if you can place your money in an investment vehicle earning an average of 4.50% per year?
2. Four years ago, Robert's annual salary was $52,500. Today, he earns $73,800. What has been the average annual rate of growth of Robert's salary?
3. You currently have $2,500 invested at an annual rate of 8%. How long will it take for this investment to grow to a value of $3,500?
4. Madison is taking over as Chief Marketing Officer at MidWest Graphics. She has pledged to increase sales from their current level of $12,000,000 at a rate of 10% per year until the firm hits sales of $20,000,000 per year. How long will it take Madison to hit the target goal at this rate of increase? )
5. The survey results from the National Association of Colleges and Employers (NACE) show the average annual increases in salaries for new accounting graduates to be 3.42% since the year 2000. If new starting salaries in accounting were $36,919 in 2000, what were they in 2020?
6. Cabot Industries invests a portion of its profits each year into a benefit emergency health care account for its employees. For the last five years it has invested year-end amounts of $50,000, $43,000, $26,000, $61,000, and $84,000. If the last deposit ($84,000) was made today and the account earns an average of 7.3% per year, how much money is currently in the account, assuming there have been no withdrawals?
7. You set aside  $100,000 at the end of each year for 20 years in equal annual end-of-the-year deposits (i.e., 20 deposits of $100,000 each, the first deposit is one year from today) into your account paying 7% interest annually. How much money will be in your account after the last deposit is made?
8. You will retire when you are 65. Which of the following choices will result in a greater future value at age 65? Choice number 1 is to invest $3,000 per year from ages 20 through 26 (a total of seven investments) into an account and then leave it untouched until you are 65 (another 39 years). Choice number 2 is to begin at age 27 and make $3,000 deposits into an investment account every year until you are 65 years old (a total of 39 investments). Each account earns an average of 10% per year. (The investments are end-of-year payments.) Explanation:  C) Choice 1:
9. You have the opportunity to lease a date palm grove in Al Ain with expected annual NET cash (after paying for expenses) from fruits of $10,000 per year for eight years. If the interest rate is 12% per year, how much maximum you would be willing to pay for leasing this property? (Hint: find the PV of these cash flows).
10. ) You have $50,000 invested in an account paying 3.50%. If you just finished paying your total college expenses for the coming year and your college costs $19,000 per year, how many years will your money last? (Treat your costs like an annuity with the first payment one year from today.)
11. You have a choice between a lottery lump sum payout of $10,000,000 today or a series of twenty-five annual annuity payments $800,000 (first payment one year from today). At an interest rate of  of 6.50%, which one do you choose?
12. Your company intends to finance the purchase of a new construction crane. The cost is $1,500,000. Compare the interest cost of three different types of loans for 10 years  (discount loan, interest only loan, amortized loan) at the interest rate of 8%.  

Answer 1

1]

future value = present value * (1 + rate of return)^{number of years}

$20,000 = present value * (1 + 4.5%)⁵

present value = $20,000 / 1.045⁵

present value = $16,049.02

2]

Ending value = starting value * (1 + growth rate)^{number of years}

$73,800 = $52,500 * (1 + growth rate)⁴

growth rate = ($73,800 / $52,500)^1/4 - 1

growth rate = 8.89%

3]

future value = present value * (1 + rate of return)^{number of years}

$3,500 = $2,500 * (1 + 8%)^{number of years}

(3500 / 2500) = 1.08^{number of years}

number of years = log_1.08(3500/2500)

number of years = 4.37 years

4]

future value = present value * (1 + rate of return)^{number of years}

$20,000,000 = $12,000,000 * (1 + 10%)^{number of years}

number of years = log_1.10(20,000,000 / 12,000,000)

number of years = 5.36 years