Question

You wish to retire in 11 years, at which time you want to have accumulated enough money to receive an annual annuity of $14,000 for 16 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 $14,000 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:

We need 11 deposits of  $ 5,268.735 per year to achieve our desired retirement plant.

Explanation:

Present value of the retirement plan in 11 years:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 14,000.00

time 16

rate 0.12

$14000 \times \frac{1-(1+0.12)^{-16} }{0.12} = PV$

PV $97,635.8061

We need to get that amount in 11 year at 10% annual rate:

$FV \div \frac{(1+r)^{time} -1}{rate} = C$

FV $97,635.8061

time 11

rate 0.1

$97635.8061183126 \div \frac{(1+0.1)^{11} -1}{0.1} = C$

C  $ 5,268.735