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