Please explain your steps You plan to retire in 30 years and want to accumulate
ID: 2654738 • Letter: P
Question
Please explain your steps
You plan to retire in 30 years and want to accumulate enough by then to provide yourself with $26,000 a year for 15 years. If the interest rate is 8%, how much must you accumulate by the time you retire? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
How much must you save each year until retirement in order to finance your retirement consumption?(Do not round intermediate calculations. Round your answer to 2 decimal places.)
Now you remember that the annual inflation rate is 3.6%. If a loaf of bread costs $1 today, what will it cost by the time you retire? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
You really want to consume $26,000 a year in real dollars during retirement and wish to save an equalreal amount each year until then. What is the real amount of savings that you need to accumulate by the time you retire? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Calculate the required preretirement real annual savings necessary to meet your consumption goals.Compare with your answer to (b). (Do not round intermediate calculations. Round your answer to 2 decimal places.)
What is the nominal value of the amount you need to save during the first year? (Assume the savings are put aside at the end of each year.) The Thirtieth year? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
You plan to retire in 30 years and want to accumulate enough by then to provide yourself with $26,000 a year for 15 years. If the interest rate is 8%, how much must you accumulate by the time you retire? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Explanation / Answer
a. This problem is of Present Value of Annuity:
Formula to calculate Present Value of Annuity Due: PV = PMT / i [1 - 1 / (1 + i)nxm ](1 + i x n)
PV = Present Value = ? PMT = Payment every Year = 26,000, i = Rate of Interest = 8%, n = Number of Years = 15, m = Compounding Frequency = 1
PV = 26,000 / 0.08 [1 -1 / (1 + 0.08)15x1 ](1 + 0.08 x 15)
PV = $240,350
So, we need to have $240,350 in the Account.
b. Formula to Calculate Future Value of Ordinay Annuity:
FV = PMT / i [(1 + i)n - 1] (1 + i)
FV = Future Value = $240,350, i = 8%, n = Number of Years = 30,
240,350 = X / 0.08 [(1 + 0.08)15 - 1](1 + 0.08)
X = $2,121.67
So, we need to save $2,121.67 evrey Year.
c) Formula to Calculate Future Value of $1:
FV = PV x (1 + i)n
FV = 1 x (1 + 0.036)30
FV = 2.89
So, the Bread will cost $2.89 at that time.