Answer:
1. = $1,485.58
2. = $1,524.21
3. = $1,545.05
4. = $1,559.56
Step-by-step explanation:
The amount the $600 will grow can be calculated using the following compounding formula:
A = P × [1 + (r ÷ n)]^nt ............................................. (1)
where:
P = Initial or original amount = $600
A = new amount
r = interest rate = 12% = 0.12
n = compounding frequency
t = overall length of period the interest is applied
Equation can then be applied as follows:
1. For 12% compounded annually for 8 years
P = Initial or original amount = $600
r = interest rate = 12% = 0.12
n = compounding frequency = annually = 1
t = overall length of period the interest is applied = 8
Therefore,
A = $600 × [1 + (0.12 ÷ 1)]^(1 × 8)
= $600 × [1 + (0.12)]^8
= $600 × (1.12)^8
= $600 × 2.47596317629481
= $1,485.58
2. For $12% compounded semiannually for 8 years.
P = Initial or original amount = $600
r = interest rate = 12% = 0.12
n = compounding frequency = semiannually = 2
t = overall length of period the interest is applied = 8
Therefore,
A = $600 × [1 + (0.12 ÷ 2)]^(2 × 8)
= $600 × [1 + (0.06)]^16
= $600 × (1.06)^16
= $600 × 2.54035168468567
= $1,524.21
3. For $12% compounded semiannually for 8 years.
P = Initial or original amount = $600
r = interest rate = 12% = 0.12
n = compounding frequency = quarterly = 4
t = overall length of period the interest is applied = 8
Therefore,
A = $600 × [1 + (0.12 ÷ 4)]^(4 × 8)
= $600 × [1 + (0.03)]^32
= $600 × (1.03)^32
= $600 × 2.57508275568511
= $1,545.05
4. For $12% compounded monthly for 8 years.
P = Initial or original amount = $600
r = interest rate = 12% = 0.12
n = compounding frequency = quarterly = 12
t = overall length of period the interest is applied = 8
Therefore,
A = $600 × [1 + (0.12 ÷ 12)]^(12 × 8)
= $600 × [1 + (0.01)]^96
= $600 × (1.01)^96
= $600 × 2.59927292555939
= $1,559.56
The observed pattern of FVs occur because of the different compounding frequency.
All the best.