Question

You wish to retire in 14 years, at which time you want to have accumulated enough money to receive an annual annuity of $17,000 for 19 years after retirement. During the period before retirement you can earn 8 percent annually, while after retirement you can earn 10 percent on your money.

 

What annual contributions to the retirement fund will allow you to receive the $17,000 annuity? Use Appendix C and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.

 

Answer 1

Annuity is the regular fixed payment over a fixed period of time.

The present value (PV) of annuity will be calculated as follows:

Here,

The annuity payment is A

The interest rate is i

The annuity period is n

The future value of annuity is calculated as follows:

Here,

The annuity payment is A

The interest rate is i

The annuity period is n

Step 1: Calculate the Retirement fund

After retirement, the required annuity is $17,000 per year for 19 years. And the required rate of return is 10%.

Calculate the present value of annuity of $17,000 per year with 10% required rate of return (discount rate after retirement) for 19 years as follows:

Therefore, the present value of annuity will be .

This is the retirement fund need to be accumulated in 14 years, so that a person can get regular annual payments of $17,000 for 19 years after retirement.

Step 2:

A person needs to contribute regular annual amount (annuity) for 14 years to accumulate the retirement fund as calculated above (142,203.641559), so that he can get $17,000 annual payment for 19 years.

Calculate the annual contribution to accumulate the amount in 14 years with the required rate of return (discount rate before retirement) of 8% or 0.08 per annum:

Therefore, the annual contribution per year until the retirement will be , so that a person can accumulate the retirement fund of to get the annual payments of $17,000 for 19 years after retirement.