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Chapter 4 Solutions
Algebra and Trigonometry (MindTap Course List)
- Depreciation Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year’s value. If a new car was purchased for $20,000, the value at the end of the first year would be $20000(0.90) and the value of the car after the end of the second year would be $20000(0.90)2. Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.arrow_forwardAn Uncertain Investment Suppose you invested 1300 in the stock market two years ago. During the first year the value of the stock increased by 12%. During the second year, the value of the stock decreased by 12%. How much money is your investment worth at the end of the two-year period? Did you earn money or lose money? Note: The answer to the first question is not 1300arrow_forwardAllan invested $10,000 in a mutual fund. If the interest rate is 5%, how much will be in the account in 15 years by each method of compounding? compound quarterly compound monthly compound continuouslyarrow_forward
- Compound Interest Use the formula A=P1+rnnt to calculate the balance A of an investment when P=$3000, r=6 and t=10years, and compounding is done (a) by the day, (b) by the hour, (c) by the minute, and (d) by the second. Does increasing the number of compoundings per year result in unlimited growth of the balance? Explain.arrow_forwardDepreciation A tool and die company buys a machine for $175,000 and it depreciates at a rate of 30 per year. (In other words, at the end of each year the depreciated value is 70 of what it was at the beginning of the year.) Find the depreciated value of the machine after 5 full years.arrow_forwardLending Money For a certain loan, the interest I due at the end of a loan period is given by I=Prt, where P is the principal barrowed, r is the yearly interest rate as a decimal, and t is the number of years since the money was barrowed. What interest is accrued if 3 years ago we barrowed 5000 at an interest rate of 5%?arrow_forward
- Megan invested $21,000 in a savings account. If the interest rate is 5%, how much will be in the account in 8 years by each method of compounding? a. compound quarterly b. compound monthly c. compound continuously.arrow_forwardGive the present value of compound interest formula where PV is the present value (in dollars), FV is the future value (in dollars), r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years. PV = ____________________ An account earns 9% interest compounded quarterly to yield $10,000 in 4 years. Determine the following values. FV = R = n = t = How much money (in dollars) should be invested when the account is opened to produce this result? (Round your answer to the nearest cent.)arrow_forwardAn investment grows according to the formula B = 8000 x 1.0085¹ dollars, where it is time, measured in months. In parts (b) and (c), round your answer to the nearest whole month. (a) What was the initial balance of the investment? $ (b) How many months does it take for the balance to double? months (c) How many more months does it take for the balance to double again? monthsarrow_forward
- I need help with the 4th and 5th questions.arrow_forwardIf $11,000 is invested at 6% interest compound monthly, find the interest earned in 18 years. The interest earned in 18 years is $_________.arrow_forwardBusiness and finance texts refer to the value of an investment at a future time as its future value. If an investment of P dollars is compounded yearly at an interest rate of r as a decimal, then the value of the investment after t years is given by the formula below. Future value = P ✕ (1 + r)t In this formula, (1 + r) t is known as the future value interest factor, so the formula above can also be written Future value = P ✕ Future value interest factor. Financial advisors sometimes use a rule of thumb known as the Rule of 72 to get a rough estimate of the time it takes for an investment to double in value. For an investment that is compounded yearly at an interest rate of r%, this rule says it will take about 72/r years for the investment to double. In this calculation, r is the integer interest rate rather than a decimal. Thus, if the interest rate is 8%, we would use 72/8 rather than 72/0.08.For the remainder of this exercise, we will consider an investment that is compounded…arrow_forward
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