Question

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

Answer 1

Answer:

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.