Final answer:
The accumulated value of $100 invested at 6.3% interest, compounded annually for 20 years, can be calculated using the compound interest formula for various compounding periods: annually, semi-annually, quarterly, and monthly. While the principal and rate remain consistent, the different compounding frequencies yield different amounts due to more frequent application of interest.
Step-by-step explanation:
The accumulated value of $100 invested at 6.3% per annum for 20 years can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
For part (a), compounded annually (n=1):
- A = $100(1 + 0.063/1)^(1*20) = $100(1.063)^20
For part (b), compounded semi-annually (n=2):
- A = $100(1 + 0.063/2)^(2*20) = $100(1.0315)^40
For part (c), compounded quarterly (n=4):
- A = $100(1 + 0.063/4)^(4*20) = $100(1.01575)^80
For part (d), compounded monthly (n=12):
- A = $100(1 + 0.063/12)^(12*20) = $100(1.00525)^240
Note: You would need to use a calculator to find the numerical value for each compound scenario.