what are the compound amount and compund interest at the end of three years if birr 10,000 is borrowed at annual interest rate of 8%
A compound monthly?
B compound quarterly?
C compounded semi annually?
D compounded annually?
E compounded continously?
To calculate the compound amount and compound interest at different compounding frequencies, we can use the formula:
Compound Amount (A) = P*(1 + r/n)^(n*t)
Where:
P = principal amount (10,000 Birr)
r = annual interest rate (0.08)
n = number of times interest is compounded per year
t = time in years (3 years)
Compound Interest = Compound Amount - Principal
A) Compound monthly (n = 12)
A = 10000 * (1 + 0.08/12)^(12*3)
A ≈ 12686.05 Birr
Compound Interest ≈ 12686.05 - 10000 = 2686.05 Birr
B) Compound quarterly (n = 4)
A = 10000 * (1 + 0.08/4)^(4*3)
A ≈ 12712.43 Birr
Compound Interest ≈ 12712.43 - 10000 = 2712.43 Birr
C) Compounded semi-annually (n = 2)
A = 10000 * (1 + 0.08/2)^(2*3)
A ≈ 12736.64
Compound Interest ≈ 12736.64 - 10000 = 2736.64
D) Compounded annually (n = 1)
A = 10000 * (1 + 0.08)^(3)
A = 12597.12
Compound Interest ≈ 12597.12 - 10000 = 2597.12
E) Compounded continuously
Using the formula A = P * e^(r*t)
A = 10000 * e^(0.08*3)
A ≈ 12749.78
Compound Interest ≈ 12749.78 - 10000 = 2749.78
Results:
A: Compound Amount ≈ 12686.05 Birr, Compound Interest ≈ 2686.05 Birr
B: Compound Amount ≈ 12712.43 Birr, Compound Interest ≈ 2712.43 Birr
C: Compound Amount ≈ 12736.64 Birr, Compound Interest ≈ 2736.64 Birr
D: Compound Amount ≈ 12597.12 Birr, Compound Interest ≈ 2597.12 Birr
E: Compound Amount ≈ 12749.78 Birr, Compound Interest ≈ 2749.78 Birr