a) Enter your desired amount of money you wish to receive each month while retired = $ 2000
b) Upon retirement (40 years from now) you want to receive "x dollars" (amount of money you choose in Part a) each month for a period of 28 years. This money resides in an account that pays 6.2% interest. How much money must be in the account to fulfill your goal?
c) You plan to deposit money every month for 40 years into an account that pays 6%. What monthly deposit must you make to achieve the amount of money determined in the answer to Part b above?
d) How much money did you actually deposit into the account?
e) How much money will you actually receive in payments during retirement?
f) You wait until later to start saving for retirement, and so are depositing money every month for only 20 years into an the same account that still pays 6%. What monthly deposit must you make to achieve the amount of money determined in the answer to Part b above?
g) How much money did you actually deposit in this plan?
h) How many times more costly is the monthly payment of Plan 2 (saving for 20 years) compared to Plan 1 (saving for 40 years)?
a) To find the amount of money needed to receive $2000 each month for 28 years with an interest rate of 6.2%, we can use the present value of an ordinary annuity formula:
PV = PMT * (1 - (1 + r)^(-n)) / r
where PV is the present value, PMT is the monthly payment, r is the interest rate per period, and n is the number of periods. In this case, PMT = $2000, r = 6.2% = 0.062, and n = 28 * 12 = 336.
Substituting the values into the formula:
PV = 2000 * (1 - (1 + 0.062)^(-336)) / 0.062
Now we can calculate the present value.
b) Using the formula from Part a), we can calculate the amount of money that needs to be in the account to fulfill the goal:
PV = 2000 * (1 - (1 + 0.062)^(-336)) / 0.062
Let's find the value of PV.
c) To find the monthly deposit needed to achieve the amount determined in Part b) for a 40-year period with a 6% interest rate, we can use the future value of an ordinary annuity formula:
FV = PMT * ((1 + r)^n - 1) / r
where FV is the future value, PMT is the monthly deposit, r is the interest rate per period, and n is the number of periods. In this case, FV = PV (calculated from Part b), r = 6% = 0.06, and n = 40 * 12 = 480.
Substituting the values into the formula:
PV = PMT * ((1 + 0.06)^480 - 1) / 0.06
Now we can calculate the monthly deposit.
d) In this case, we need to find the total amount of money deposited into the account over the 40-year period. This can be calculated by multiplying the monthly deposit (calculated in Part c) by the number of periods (40 * 12 = 480).
Total deposited = PMT * 480
Let's calculate the total deposited.
e) To calculate the total amount of money received in payments during retirement, we need to multiply the monthly payment ($2000) by the number of payment periods (28 * 12 = 336).
Total received = PMT * 336
Let's calculate the total received.
f) To find the monthly deposit needed to achieve the amount determined in Part b) for a 20-year period with a 6% interest rate, we can use the same formula as in Part c), with n = 20 * 12 = 240.
PV = PMT * ((1 + 0.06)^240 - 1) / 0.06
Now we can calculate the monthly deposit.
g) Similar to Part d), we need to find the total amount of money deposited into the account over the 20-year period. This can be calculated by multiplying the monthly deposit (calculated in Part f) by the number of periods (20 * 12 = 240).
Total deposited = PMT * 240
Let's calculate the total deposited.
h) To find the ratio of the monthly payment of Plan 2 (saving for 20 years) compared to Plan 1 (saving for 40 years), we divide the total deposited for Plan 2 by the total deposited for Plan 1.
Ratio = Total deposited Plan 2 / Total deposited Plan 1
Let's calculate the ratio.