Find the future values of these ordinary annuities. Compounding occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent. $900 per year for 12 years at 10%. $ 19,245.85 $450 per year for 6 years at 5%. $ 3,060.86 $200 per year for 6 years at 0%. $ Rework parts a, b, and c assuming they are annuities due. Future value of $900 per year for 12 years at 10%: $ 21,170.43 Future value of $450 per year for 6 years at 5%: $ 3,213.90 Future value of $200 per year for 6 years at 0%: $

a. Futuere Value = $19,245.86

b. Futuere Value = $3,060.86

c. Futuere Value = $0

d-1. Futuere Value = $21,170.44

d-2. Futuere Value = $3,213.90

d-3. Futuere Value = $0

Explanation:

Note: The data in the question are merged. They are therefore sorted before answering the question as follows:

Find the future values of these ordinary annuities. Compounding occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.

a. $900 per year for 12 years at 10%. $ 19,245.85

b. $450 per year for 6 years at 5%. $ 3,060.86

c. $200 per year for 6 years at 0%. $

d. Rework parts a, b, and c assuming they are annuities due.

Future value of $900 per year for 12 years at 10%: $ 21,170.43

Future value of $450 per year for 6 years at 5%: $ 3,213.90

Future value of $200 per year for 6 years at 0%: $

Explanation of the answer is now provided as follows:

The formula for calculating the Future Value (FV) of an Ordinary Annuity given as follows:

FV = M * (((1 + r)^n - 1) / r) (1)

Where,

FV = Future value of the amount =?

M = Annuity payment

r = Annual interest rate

n = number of periods years

This formula is now applied as follows:

a. $900 per year for 12 years at 10%. $ 19,245.85

Therefore, we have:

FV = ?

M = $900

r = 10%, or 0.10

n = 12

Substituting the values into equation (1), we have:

FV = $900 * (((1 + 0.10)^12 - 1) / 0.10)

FV = $900 * 21.38428376721

FV = $19,245.855390489

Rounding the nearest cent, we have:

FV = 19,245.86

b. $450 per year for 6 years at 5%. $ 3,060.86

Therefore, we have:

FV = ?

M = $450

r = 5%, or 0.05

n = 6

Substituting the values into equation (1), we have:

FV = $450 * (((1 + 0.05)^6 - 1) / 0.05)

FV = $450 * 6.8019128125

FV = $3,060.860765625

Rounding the nearest cent, we have:

FV = $3,060.86

c. $200 per year for 6 years at 0%. $

Therefore, we have:

FV = ?

M = $200

r = 0%, or 0

n = 6

Substituting the values into equation (1), we have:

FV = $200 * (((1 + 0)^6 - 1) / 0)

FV = $200 * ((1^6 - 1) / 0)

FV = $200 * ((1 - 1) / 0)

FV = $200 * (0 / 0)

FV = $200 * 0

FV = $0

d. Rework parts a, b, and c assuming they are annuities due.

The formula for calculating the Future Value (FV) of an Annuity Due is given as follows:

FV = M * (((1 + r)^n - 1) / r) * (1 + r) (2)

Where,

FV = Future value

M = Annuity payment

r = Annual interest rate

n = number of periods years

This formula is now applied as follows:

d-1. Future value of $900 per year for 12 years at 10%: $ 21,170.43

Therefore, we have:

FV = ?

M = $900

r = 10%, or 0.10

n = 12

Substituting the values into equation (2), we have:

FV = $900 * (((1 + 0.10)^12 - 1) / 0.10) * (1 + 0.10)

FV = $900 * 21.38428376721 * 1.10

FV = $2,1170.4409295379

Rounding the nearest cent, we have:

FV = $2,1170.44

d-2. Future value of $450 per year for 6 years at 5%: $ 3,213.90

Therefore, we have:

FV = ?

M = $450

r = 5%, or 0.05

n = 6

Substituting the values into equation (2), we have:

FV = $450 * (((1 + 0.05)^6 - 1) / 0.05) * (1 + 0.05)

FV = $450 * 6.8019128125 * 1.05

FV = $3,213.90380390625

Rounding the nearest cent, we have:

FV = $3,213.90

d-3. Future value of $200 per year for 6 years at 0%: $

Therefore, we have:

FV = ?

M = $200

r = 0%, or 0

n = 6

Substituting the values into equation (2), we have:

FV = $200 * (((1 + 0)^6 - 1) / 0) * (1 + 0)

FV = $200 * ((1^6 - 1) / 0) * 1

FV = $200 * ((1 - 1) / 0) * 1

FV = $200 * (0 / 0) * 1

FV = $200 * 0 * 1

FV = $0

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