Find the amount to which $600 will grow under each of these conditions: 12% compounded annually for 8 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ 12% compounded semiannually for 8 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ 12% compounded quarterly for 8 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ 12% compounded monthly for 8 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ 12% compounded daily for 8 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ Why does the observed pattern of FVs occur

1. = $1,485.58

2. = $1,524.21

3. = $1,545.05

4. = $1,559.56

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.