Question

You have just turned 22 years old, recieved your bacheor's degree, and accepetd your first job, Now you must decide how much money to put into your retirement plan. The plan works as follows: Every dollar in the plan earns 7.5% per year. You cannot make withdrawls until you retire on your 65th birthday. After that, you can make withdrawls as you see fit. You decide that you will plan to live to 100 and work until you turn 65. You estimate that to live comforatbly in retirement, you will need $95,000 per year, starting at the end of the first year of retirement and ending on your 100th birthday. You will contribute the same amount to the plan at the end of every year that you work. How much do you need to contribute each year to fund your retirement?

Your annual contribution should be $_______ (Round to the nearest cent)

Answer 1

Time till retirement , n = 65-22 = 43 years

Interest, R = 7.5% = 0.075

amount needed per year after retirement, A = 95000

time period for receiving amount A = t =100 - 65 = 35 years

Present Value at the end of 65 years ( of annual amount 95000) = A*PVIFA

PVIFA =present value interest rate factor of annuity = ((1+R)^t-1)/((1+R)^t*R) = ((1.075)³⁵-1)/((1.075)³⁵*0.075) = 12.27251141

Present Value at the end of 65 years ( of annual amount 95000) = A*PVIFA = 95000*12.27251141 = 1,165,888.58426

The present value caculated above is the future value of the total amount from retirement plan

Future value(FV) of retirement plan =  1,165,888.58426

FV = A*FVIFA

FVIFA = future value interest rate factor of annuity

= ((1+R)ⁿ-1)/(R) = ((1.075)⁴³-1)/0.075 = 21.41630168/0.075 = 285.5506891

FV = A *FVIFA = A*285.5506891

FV = 1,165,888.58426

Substituting FV in the above equation

1,165,888.58426 = A*285.5506891

A = 1,165,888.58426/285.5506891 = $4082.947892

This is the annual contribution required

Thus Annual contribution = $4082.947892 or 4082.95 ( rounding off to 2 decimal points) or 4082.9 ( rounding off to 1 decimal point)