1-a. The amount that will be in your account at the end of 6 years is $11,643.14.
1-b. The amount that will be in your account at the end of 6 years is $11,992.43.
2-a. The amount you need in your retirement account the day you retire is $590,938.17.
2-b. The amount you need in your retirement account the day you retire is $679,578.89.
Explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
1. You plan to deposit $1,800 per year for 6 years into a money market account with an annual return of 3%. You plan to make your first deposit one year from today.
a. What amount will be in your account at the end of 6 years? Round your answer to the nearest cent. Do not round intermediate calculations.
b. Assume that your deposits will begin today. What amount will be in your account after 6 years? Round your answer to the nearest cent. Do not round intermediate calculations.
2. You and your wife are making plans for retirement. You plan on living 30 years after you retire and would like to have $90,000 annually on which to live. Your first withdrawal will be made one year after you retire and you anticipate that your retirement account will earn 15% annually.
a. What amount do you need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations.
b. Assume that your first withdrawal will be made the day you retire. Under this assumption, what amount do you now need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations.
The explanation of the answers is now provided as follows:
1-a. What amount will be in your account at the end of 6 years? Round your answer to the nearest cent. Do not round intermediate calculations.
Since you plan to make your first deposit one year from today, this can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:
FV = D * (((1 + r)^n - 1) / r) (1)
Where,
FV = Future value or the amount that will be in your account at the end of 6 years = ?
D = Annual deposit = $1,800
r = Annual return rate = 3%, or 0.03
n = number of periods = 6
Substituting the values into equation (1), we have:
FV = $1,800 * (((1 + 0.03)^6 - 1) / 0.03) = $11,643.14
Therefore, the amount that will be in your account at the end of 6 years is $11,643.14.
1-b. Assume that your deposits will begin today. What amount will be in your account after 6 years? Round your answer to the nearest cent. Do not round intermediate calculations.
Since it is assumed that your deposits will begin today, this can be calculated using the formula for calculating the Future Value (FV) of an Annuity Due as follows:
FV = M * (((1 + r)^n - 1) / r) * (1 + r) (2)
Where,
FV = Future value or the amount that will be in your account at the end of 6 years = ?
D = Annual deposit = $1,800
r = Annual return rate = 3%, or 0.03
n = number of years = 6
Substituting the values into equation (2), we have:
FV = $1,800 * (((1 + 0.03)^6 - 1) / 0.03) * (1 + 0.03) = $11,992.43
Therefore, the amount that will be in your account at the end of 6 years is $11,992.43.
2-a. What amount do you need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations.
Since your first withdrawal will be made one year after you retire, this can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (3)
Where:
PV = Present value or the amount you need in your retirement account the day you retire = ?
P = Annual withdrawal = $90,000
r = Annual return rate = 15%, or 0.15
n = number of years = 30
Substituting the values into equation (3), we have:
PV = $90,000 * ((1 - (1 / (1 + 0.15))^30) / 0.15) = $590,938.17
Therefore, the amount you need in your retirement account the day you retire is $590,938.17.
2-b. Assume that your first withdrawal will be made the day you retire. Under this assumption, what amount do you now need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations.
Since it is assumed that that your first withdrawal will be made the day you retire, this can be determined using the formula for calculating the present value of an annuity due as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) * (1 + r) …………………………………. (4)
Where:
PV = Present value or the amount you need in your retirement account the day you retire = ?
P = Annual withdrawal = $90,000
r = Annual return rate = 15%, or 0.15
n = number of years = 30
Substituting the values into equation (4), we have:
PV = $90,000 * ((1 - (1 / (1 + 0.15))^30) / 0.15) (1 + 0.15) = $679,578.89
Therefore, the amount you need in your retirement account the day you retire is $679,578.89.
