Respuesta :
Given Information:
Annual interest rate = r = 12%
Principal amount = P = $1000
Number of years = t = 3
Required Information
Accumulated amount = A = ?
Answer:
Annual compounding = A = $1404.93
Semi-annuall compounding = A = $1418.52
Quarterly compounding = A = $1425.76
Monthly compounding = A = $1432.30
Daily compounding = A = $1433.14
Step-by-step explanation:
The accumulated amounts in terms of compound interest is given by
[tex]A = P(1 + i)^N[/tex]
Where P is the initial amount invested and A is the accumulated amount.
For annual compounding:
i = 0.12
N = 3
[tex]A = 1000(1 + 0.12)^3 \\\\A = \$ 1404.93[/tex]
For semiannually compounding:
i = 0.12/2 = 0.06
N = 2*3 = 6
[tex]A = 1000(1 + 0.06)^6 \\\\A = \$ 1418.52[/tex]
For quarerterly compounding:
i = 0.12/4 = 0.03
N = 4*3 = 12
[tex]A = 1000(1 + 0.03)^12 \\\\A = \$ 1425.76[/tex]
For monthly compounding:
i = 0.12/30 = 0.004
N = 30*3 = 90
[tex]A = 1000(1 + 0.004)^90 \\\\A = \$ 1432.30[/tex]
For daily compounding:
i = 0.12/365 = 0.0003287
N = 365*3 = 1095
[tex]A = 1000(1 + 0.0003287)^1095 \\\\A = \$ 1433.14[/tex]
