Assume that you have 40 years until retirement and have just started your first
ID: 2761443 • Letter: A
Question
Assume that you have 40 years until retirement and have just started your first job. Once you retire, you anticipate that you will live for 30 additional years. Assume that you will require $100,000 per year to support yourself in retirement. All investments that you make will go into and stay in an account that returns 7% per year (i.e. however much you have at retirement will sit in that account and continue to accrue interest on the remaining balance.) How much will you have to save each year over the next 40 years to meet your goal? Assume that your first investment occurs at the end of your first year of work (yr 1) and that the last of your 40 investments occurs on the last day that you are employed (yr 40). For simplicity, assume that your first withdrawal is at the end of your first retirement year (yr 41)
Explanation / Answer
Ans;
Future value of savings at end of year 40 = Present value of cash outflows for 30 years beginning at end of year 41
PV of future cash out flows C*[(1-(1+i/100)^(-n))/(i/100)]
C = Cash flow per period
i = interest rate
n = number of payments
PV = 100000*[(1 - (1+ 8/100)^(-30))/(8/100)]
Future value of cash inflows
FV of annuity = C* ( ((1 + i )^n -1)/i)
C = Cash flow per period
i = interest rate
n = number of payments
FV = X *[((1+ 8/100)^40 -1)/(8/100)]
FV = PV
X *(((1+ 8/100)^40 -1)/(8/100)) = 100000*((1 - (1+ 8/100)^(-30))/(8/100))
X = (100000*((1 - (1+ 8/100)^(-30))/(8/100)))/(((1+ 8/100)^40 -1)/(8/100)) =
4345.686