Answer:
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