Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 5000
r = 4% = 4/100 = 0.04
t = 3 years
1) compounded annually
n = 1 because it was compounded once in a year.
Therefore,
A = 5000(1 + 0.04/1)^1 × 3
A = 5000(1.04)^3
A = $5624.32
2) compounded semi annually
n = 2 because it was compounded twice in a year.
Therefore,
A = 5000(1 + 0.04/2)^2 × 3
A = 5000(1.02)^6
A = $5630.81
3) compounded quarterly
n = 4 because it was compounded 3 times in a year and n = 12/3 = 4.
Therefore,
A = 5000(1 + 0.04/4)^4 × 3
A = 5000(1.01)^12
A = $5634.13
4) compounded monthly
n = 12 because it was compounded 12 times in a year.
Therefore,
A = 5000(1 + 0.04/12)^12 × 3
A = 5000(1.0033)^36
A = $5629.62
The amount that will there be in the account after 3 years if the interest is:
Using this formula
A = P(1 + r/n)^nt
Where:
P = 500
r = 4% or 0.04
t = 3 years
1. Annually
A = 5000(1 + 0.04/1)^1 × 3
A = 5000(1.04)^3
A = $5624.32
2. Semi annually
A = 5000(1 + 0.04/2)^2 × 3
A = 5000(1.02)^6
A = $5630.81
3. Quarterly
A = 5000(1 + 0.04/4)^4 × 3
A = 5000(1.01)^12
A = $5634.13
4. Monthly
A = 5000(1 + 0.04/12)^12 × 3
A = 5000(1.0033)^36
A = $5629.62
Inconclusion the amount that will there be in the account after 3 years if the interest is: Compounded annually $5624.32.
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