Question

Assume that you want to see how much money you will receive each year during retirement in today’s dollars. You are currently 30 and 35 years from retirement. You plan on putting away $8,000 at the end of each year until retirement. You expect to receive a 9.6% return on your retirement savings. At the end of 35 years you believe that you will live until the age of 75 (10 years). At the age of 75 you believe that you will die and not have any money in your retirement left. In retirement you will shift your retirement savings to a safer choice, a savings bond. You believe savings bonds at the age of 65 will be 2.5% per year. Based on the information above how much would you receive each year? If the inflation rate is 3.2%, what is the present value of your first payment in retirement in today’s dollars (meaning what is the first payment when you bring the payment back 35 years at an inflation rate of 3.2%).

Answer 1

To calculate the amount at the end of retirement, we will use the Future Value annuity formula

Future value(Annuity) = P(((1+r)^n-1)/r)

P = Periodic Payment = $8,000
r= Rate of interest = 9.6%
n = number of years = 35

Future Value = 8,000(((1+0.096)^35 - 1)/0.096) = $1,978,189.50

Hence amount at the end of retirement = $1,978,189.50

Such amount will be invested in savings bonds that will fetch 2.5% and since at the end of 75 no amount will be left, amount wil be drawn in 10 years

Present Value(Annuity) = P((1-(1+r)^-n)/r)

Present Value = $1,978,189.50
P= ?
r= rate of interest = 2.5%
n = no of years = 10

$1,978,189.50= P((1-(1+.025)^-10)/.025)
P = $226,025.50

Hence we will receive $226,025.50 annually.

The present value of the amount that will be received after 35 years @3.2%

Present Value = P(1/(1+r)^n)
P = Amount = $226,025.50​
r= rate of interest = 3.2%
n = no of years =35 years

Present Value = $226,025.50(1/(1+.032)^35)
Present Value = $75,053