High School

1. Today you deposited $5,000 into a savings account paying 12% interest. How much should you have in 15 years?

2. A loaf of bread today costs $1.28. If grocery prices are going up at the rate of 8% per year, how much will a loaf of bread cost in 6 years?

3. The average price of new homes is $138,500. If new home prices are increasing at a rate of 15% per year, how much will a new home cost in 12 years?

4. You deposit $3,500 into an account every year for 6 years. The account pays 7% interest. How much will you have at the end of that time?

5. You deposit $4,000 each year into a retirement account paying 8% interest. How much will you have in 25 years when you retire?

6. What is the present value of $5,000 to be received in 7 years at an interest rate of 7%?

7. You can buy a parcel of real estate today that you estimate will bring $15,000 in 9 years. Assuming your money is worth 9%, how much would you be willing to pay for the property?

8. An insurance company is willing to settle a dispute with you. They will pay you $7,000 per year for the next 8 years, or one lump sum right now. Assuming your money is worth 5%, how much would you be willing to settle for?

9. You currently receive $10,000 per year on a contract. You expect it to run another 7 years. Someone wants to buy the contract from you. If you can earn 12% on other investments of this quality, how much would you be willing to sell the contract for?

10. You can insulate your home for $7,200. You figure you can save 15% per year on your heating bill if you insulate. Your home was bought 15 years ago for $38,500. You figure real estate prices have gone up 16% each year. You plan to live in the house another 10 years. Your home has five bedrooms, 2,367 square feet, and requires 5,400 BTUs per hour to heat. You heat with oil and use 175 barrels of oil per year. Oil currently costs $25 per barrel. Money is worth 5% to you. Should you insulate your home? Why?

Answer :

Final Answers:

1. After 15 years, you should have approximately $18,856.06 in the savings account.

2. In 6 years, a loaf of bread will cost approximately $1.71.

3. In 12 years, a new home will cost approximately $454,977.69.

4. At the end of 6 years, you will have approximately $24,033.46 in the account.

5. When you retire in 25 years, you will have approximately $247,091.75 in the retirement account.

6. The present value of $5,000 to be received in 7 years at an interest rate of 7% is approximately $3,480.80.

7. You would be willing to pay approximately $6,785.14 for the property.

8. You would be willing to settle for a lump sum of approximately $45,978.55.

9. You would be willing to sell the contract for approximately $51,601.86.

10. Yes, you should insulate your home.

Explanation:

1. To calculate the future value of a deposit of $5,000 into a savings account paying 12% interest for 15 years, you can use the formula for compound interest: [tex]A = P(1 + r/n)^{(nt)[/tex], where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the values, you get [tex]A = $5,000(1 + 0.12/1)^{(1*15)[/tex] = $18,856.06.

2. To find the cost of a loaf of bread in 6 years with an 8% annual price increase, you can use the formula for compound interest as well. The future cost (C) is $1.28(1 + 0.08)⁶ = $1.71.

3. For the new home price in 12 years with a 15% annual increase, you can use the same formula: $138,500(1 + 0.15)¹² = $454,977.69.

4. To calculate the future value of annual deposits into an account, you can use the formula for future value of an annuity: FV = [tex]PMT[(1 + r/n)^{(nt)} - 1] / (r/n)[/tex], where PMT is the annual deposit, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the values, you get FV = [tex]$3,500[(1 + 0.07/1)^{(1*6)} - 1] / (0.07/1)[/tex] = $24,033.46.

5. To determine the retirement account balance after 25 years with $4,000 annual deposits and 8% interest, you can use the annuity formula: FV =[tex]PMT[(1 + r/n)^{(nt)} - 1] / (r/n),[/tex] which yields FV = [tex]$4,000[(1 + 0.08/1)^{(1*25)} - 1] / (0.08/1)[/tex] = $247,091.75.

6. The present value of $5,000 to be received in 7 years at 7% interest is found using the present value formula: PV = [tex]FV / (1 + r/n)^{(nt)[/tex]. Plugging in the values, you get PV = [tex]$5,000 / (1 + 0.07/1)^{(1*7)} =[/tex] $3,480.80.

7. To determine the property's present value, you use the present value of a single future sum formula: PV =[tex]FV / (1 + r/n)^{(nt)[/tex]. Plugging in the values, you get PV = [tex]$15,000 / (1 + 0.09/1)^{(1*9)[/tex] = $6,785.14.

8. Calculating the present value of the insurance settlement, you can use the present value formula: PV =[tex]PMT[(1 - (1 + r)^{(-n)}) / r],[/tex] where PMT is the annual payment, r is the discount rate, and n is the number of years. Plugging in the values, you get PV = [tex]$7,000[(1 - (1 + 0.05)^{(-8)})[/tex] / 0.05] = $45,978.55.

9. To determine the contract's selling price with a 12% alternative investment rate, you can use the present value of an annuity formula: PV = [tex]PMT[(1 - (1 + r)^{(-n)}) / r][/tex], where PMT is the annual payment, r is the discount rate, and n is the number of years. Plugging in the values, you get PV = [tex]$10,000[(1 - (1 + 0.12)^{(-7)}) / 0.12] =[/tex] $51,601.86.

10. Yes, you should insulate your home because you can save 15% per year on your heating bill, which would amount to substantial savings over the next 10 years. Additionally, the rising real estate prices indicate that the investment in insulation is likely to increase your home's value, making it a wise financial decision.

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