Question

You have just turned 30 years​ old, have just received your​ MBA, and have accepted 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 9 % per year. You cannot make withdrawals until you retire on your 60 th birthday. After that​ point, you can make withdrawals as you see fit. You decide that you will plan to live to 100 and work until you turn 60. You estimate that to live comfortably in​ retirement, you will need $ 98 comma 000 per year starting at the end of the first year of retirement and ending on your one hundredth 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?

Answer 1

To fund your retirement, you would need to contribute approximately $15,945.28 each year. This calculation takes into account compound interest and the amount you estimate you will need in retirement.

Step-by-step explanation:

To determine how much you need to contribute each year to fund your retirement, you can use the concept of annuities and compound interest. An annuity is a series of equal payments made at regular intervals. In this case, you will contribute the same amount at the end of every year that you work.

First, calculate the future value of the retirement fund using compound interest. Since you will retire at 60 and plan to live to 100, you will have 40 years in retirement. Assuming a 9% annual return, you can use the formula:

Future Value = Annuity Payment x [(1 + interest rate)^(number of years) - 1] / interest rate

Substituting the values, we have:

Future Value = $98,000 x [(1 + 0.09)⁽⁴⁰⁾ - 1] / 0.09

Future Value = $98,000 x (3.172 - 1) / 0.09

Future Value = $98,000 x 2.172 / 0.09

Future Value = $98,000 x 24.1333

Future Value = $2,367,066.67

Next, you need to calculate the annuity payment. Since you will be making equal contributions every year, you can use the formula:

Annuity Payment = Future Value / [(1 + interest rate)^(number of years) - 1] / interest rate

Substituting the values, we have:

Annuity Payment = $2,367,066.67 / [(1 + 0.09)⁽³⁰⁾ - 1] / 0.09

Annuity Payment = $2,367,066.67 / (2.367 - 1) / 0.09

Annuity Payment = $2,367,066.67 / 1.367 / 0.09

Annuity Payment = $2,367,066.67 / 0.1486

Annuity Payment = $15,945.28 (rounded to the nearest cent)

Therefore, you would need to contribute approximately $15,945.28 each year to fund your retirement plan.

Answer 2

Annual deposit= $21,568.87

Step-by-step explanation:

Giving the following information:

You have just turned 30 years​ old. Every dollar in the plan earns 9 % per year. You cannot make withdrawals until you retire on your 60th birthday.

You will need $ 98,000 per year starting at the end of the first year of retirement and ending on your one-hundredth birthday.

First, we need to calculate the total amount needed at age 60.

Final value= 30years*98,000= $2,940,000

To calculate the annual deposit we need the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (2,940,000*0.09)/[(1.09^30)-1]= $21,568.87