Question

You wish to retire in 20 years, at which time you want to have accumulated enough money to receive an annual annuity of $24,000 for 25 years after retirement. During the period before retirement you can earn 10 percent annually, while after retirement you can earn 12 percent on your money. What annual contributions to the retirement fund will allow you to receive the $24,000 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

Answer:

$3,286.52

Explanation:

PVA= A×({1 −[1 / (1 + i)n]} / i)= $24,000 ×({1 −[1 / (1.12)25]} / .12)

= $188,235.34

FVA= A×{[(1 + i)n−1] / i}A=

FVA/ {[(1 + i)n−1] / i}= $188,235.34 / {[(1.10)20−1] / .10}= $3,286.52

To determine the annual deposit into an account earning 10 percent that is necessary to accumulate$188,235.34 after 20 years, solve for the annuity:

N= 20

I/Y=10

PV=0

PMT=CPT PMT -3286.52

FV=188 235.34

Answer: $3,286.52