940 Words4 Pages

Week 1: Problem Set 1
1. Ben Collins plans to buy a house for $65,000. If that real estate property is expected to increase in value 5 percent each year, what would its approximate value be seven years from now?
Answer: PV * FVF or, PV (1 + .05)^n or, PV (1.05)^7 or, PV * 1.4071 or, $65,000 * 1.4071 = $91,461.50
2. At an annual interest rate of five percent, how long would it take for your savings to double?
Answer: Future Value Factor = (1 + i)^n or, FVF = (1 + .05)^14.21 or, FVF = 2.000322: Where $1,000 * 2.000322 = $2,000.3221 or, rounded to the nearest whole dollar it would take 14.21 years with a 5% APR to double one’s savings.
3. In the mid-1990s, selected automobiles had an average cost of $12,000. The average cost of those same motor vehicles is now $20,000. What was the rate of increase for this item between the two time periods?
Answer: Using an increment of 15 years; PV * FVF or, PV (1 + i)^n or, PV (1.0347)^15 or, $12,000 * 1.6681 = $20,017.20; Alternatively, PV (1.0346)^15 or, $12,000 * 1.6657 = $19,988.40; So, we can see the rate of increase was between 3.46% and 3.47% each year for 15 years.
4. A family spends $28,000 a year for living expenses. If prices increase by 4 percent a year for the next three years, what amount will the family need for its living expenses?
Answer: PV (1 + i)^n or, PV (1 + .04)^3 or, $28,000 * 1.125 = $31,500 needed for the family’s annual living expenses.
5. What would be the yearly earnings for a person with $6,000 in savings at an annual interest rate of 5.5 percent?
Answer: PV (1 + i)^n - PV or, $6,000 * 1.055 - $6,000 = $330 in yearly earnings.
6. Elaine Romberg prepares her own income tax return each year. A tax preparer would charge her $60 for this service. Over a period of 10 years, how much does Elaine gain from preparing her own tax return? Assumes she can earn 3 percent on her savings.

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