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ACCTGUY · May 7, 2012, 07:58 PM

Ladyx is planning to retire in 25 years at which time she hopes to have accumulated enough money to receive an annuity of $ 21,000 a year for 26 years of retirement. During her pre retirement period she expects to earn 7 percent annually while during retirement she expects to earn 6 percent annually on her money. What annual contribution to this retirement fund are required for ladyx to achieve her objective.

Please show me how to solve this.
If you can give me formual which you are using that will be great

ArcSine · May 8, 2012, 03:50 AM

This one is handled in two steps, using formulas you'll find in your text.

First determine the single amount she needs to have on the first day of retirement, in order to withdraw 21,000 per year for 26 years, while the undrawn principle earns an expected 6% throughout. For this you use the Present Value of an Ordinary Annuity formula. The formula requires three inputs, which are the three given values (21,000 per year, 26 years, 6%).

In other words, with this formula you're finding X for the statement, "In order to exactly pay out 21,000 per year for 26 years, an investment fund earning 6% needs a beginning amount of X."

Having determined that single amount X needed on the first day of retirement, you'll then use the Future Value of an Ordinary Annuity formula to determine the annual amount she'll need to invest, in order to accumulate the target retirement sum in 25 years, assuming an earnings rate of 7%. In this case your known values are: The earnings rate of 7%; the total number of payments = 25; and the desired accumulated amount immediately upon the 25th payment into the fund.

Thus here you're determining Y for the statement, "In order to have X in my investment fund 25 years from today, I need to invest the amount Y into the fund every year for 25 years, with the first investment one year from today, assuming the fund will earn interest at 7% per year."

Look up those two formulas in your book and have a go at it. Post back in for a check on your answer, or if you need a bit more guidance.