Answer:
To calculate the value of the investment at the end of 5 years for different compounding methods, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the initial principal amount (36100 dollars in this case)
r = the annual interest rate (9 percent or 0.09 as a decimal)
n = the number of times interest is compounded per year
t = the number of years
(a) Annual compounding:
For annual compounding, n = 1 (compounded once per year)
A = 36100(1 + 0.09/1)^(1*5)
A ≈ 36100(1.09)^5
A ≈ 36100(1.5386246)
A ≈ 55537.33 dollars
(b) Semiannual compounding:
For semiannual compounding, n = 2 (compounded twice per year)
A = 36100(1 + 0.09/2)^(2*5)
A ≈ 36100(1.045)^10
A ≈ 36100(1.6288946)
A ≈ 58785.46 dollars
(c) Monthly compounding:
For monthly compounding, n = 12 (compounded twelve times per year)
A = 36100(1 + 0.09/12)^(12*5)
A ≈ 36100(1.0075)^60
A ≈ 36100(1.4579742)
A ≈ 52562.43 dollars
(d) Daily compounding:
For daily compounding, n = 365 (compounded 365 times per year)
A = 36100(1 + 0.09/365)^(365*5)
A ≈ 36100(1.000246575)^1825
A ≈ 36100(1.4497384)
A ≈ 52292.54 dollars
Therefore, to the nearest cent, the value of the investment at the end of 5 years for different compounding methods is as follows:
(a) Annual: $55,537.33
(b) Semiannual: $58,785.46
(c) Monthly: $52,562.43
(d) Daily: $52,292.54