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Find the future value of a five-year $96,000 investment that pays 5.50 percent and that has the following compounding periods: (Do not round intermediate calculations, round final answers to 2 decimal places, e.g. 15.25.)

Value of investment after 5 years
a.Quarterly$ b.Monthly$ c.Daily$ d.Continuous$

1 Answer

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Final answer:

The future value of a $96,000 investment after 5 years can be calculated using compound interest formulas, accounting for different compounding periods like quarterly, monthly, daily, and continuous.

Step-by-step explanation:

The value of a $96,000 investment over 5 years with various compounding periods can be found using the compound interest formula: A = P(1 + r/n)^(nt). Here, P is the principal amount ($96,000), r is the annual interest rate (5.50% or 0.055), n is the number of times the interest is compounded per year, t is the time the money is invested for in years (5 years), and A is the amount of money accumulated after n years, including interest.

  • Quarterly Compounding: For quarterly compounding, n = 4. A = 96000(1 + 0.055/4)^(4*5) = 96000(1.01375)^(20).
  • Monthly Compounding: For monthly compounding, n = 12. A = 96000(1 + 0.055/12)^(12*5) = 96000(1.0045833)^(60).
  • Daily Compounding: For daily compounding, n = 365. A = 96000(1 + 0.055/365)^(365*5) = 96000(1.000150685)^(1825).
  • Continuous Compounding: For continuous compounding, the formula is A = Pe^(rt). A = 96000 * e^(0.055*5).

Calculating these values will give the future value of the investment for each compounding period:

  1. Quarterly: $96,000(1.01375)^(20) = $125,778.77
  2. Monthly: $96,000(1.0045833)^(60) = $126,010.79
  3. Daily: $96,000(1.000150685)^(1825) = $126,158.29
  4. Continuous: $96,000 * e^(0.055*5) = $126,242.99

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