Question

8. You plan to retire in 35 years and can invest to earn 6.85 percent. You estimate that you will need $82,000 at the end of each year for an estimated 30 years after retirement, and you expect to earn 4.5 percent during those retirement years. How much do you need to set aside at the end of each year to accumulate the money necessary for your retirement? (Assume year-end cash flows.) I will need this much at retirement _____________and will need to set aside ___________per year (at the end of each year.

Answer 1

Step - 1 ............. Compute the present value of 30 years Post retirement cash flows.

That means Last 30 years on the time line of 65 years.

= Annuity * ( 1 - (1+r)^-n ) / r

= 82000 * ( 1 - ( 1.045) ^-30 ) / 0.045

= 1,335,688.86

This means that, I will need this much at retirement 1,335,688.86

Step - 2

FVIFA = Future value of Interest factor annuity = [ (1+r)ⁿ - 1 ] / r = [ ( 1.0685)³⁵ - 1 ] / 0.0685

= 133.79597734

Annual deposit needed = 1,335,688.86 / 133.79597734 = 9983.03

I will need this much at retirement 1,335,688.86 and will need to set aside 9983.03 per year (at the end of each year.