Business 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 yearly at an interest rate of 13%. (a) According to the Rule of 72, how long will it take the investment to double in value? (Round your answer to two decimal places.) yr Parts (b) and (c) of this exercise will check to see how accurate this estimate is for this particular case. (b) Using the answer you got from part (a) of this exercise, calculate the future value interest factor. (Round your answer to two decimal places.) Is it exactly the same as the future value interest factor that would make an investment double, found from using the formula for future value? YesNo (c) If your initial investment was $4000, use your answer from part (b) to calculate the future value. (Round your answer to two decimal places.) $ Did your investment exactly double? YesNo

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Business 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 yearly at an interest rate of 13%.

(a) According to the Rule of 72, how long will it take the investment to double in value? (Round your answer to two decimal places.)
yr

Parts (b) and (c) of this exercise will check to see how accurate this estimate is for this particular case.

(b) Using the answer you got from part (a) of this exercise, calculate the future value interest factor. (Round your answer to two decimal places.)

Is it exactly the same as the future value interest factor that would make an investment double, found from using the formula for future value?

YesNo

(c) If your initial investment was $4000, use your answer from part (b) to calculate the future value. (Round your answer to two decimal places.)
$

Did your investment exactly double?

YesNo

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