Respuesta :
Answer:
The future value of the same annuity due is $10,400.
Explanation:
Step 1: Calculation of the annuity payment
This can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:
FV = P * (((1 + r)^n - 1) / r) ................................. (1)
Where,
FV = Future value of the amount after 7 years = $10.000
P = Annuity payment = ?
r = interest rate = 4%, or 0.04
n = number of years = 7
Substituting the values into equation (1) and solve for P, we have:
10,000 = P * (((1 + 0.04)^7 - 1) / 0.04)
10,000 = P * 7.89829448089601
P = 10,000 / 7.89829448089601
P = $1,266.09612039504
Step 2: Calculation of the future value of the same annuity due
This can be calculated using the formula for calculating the Future Value (FV) of an Annuity Due as follows:
FV = P * (((1 + r)^n - 1) / r) * (1 + r) ................................. (2)
Where,
FV = Future value the same annuity due = ?
P = Annuity payment as obtained in Step 1 above = $1,266.09612039504
r = interest rate = 4%, or 0.04
n = number of years = 7
Substituting the values into equation (2), we have:
FV = $1,266.09612039504 * (((1 + 0.04)^7 - 1) / 0.04) * (1 + 0.04)
FV = $1,266.09612039504 * 7.89829448089601 * 1.04
FV = $10,400
Therefore, the future value of the same annuity due is $10,400.
