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

Answer 1

$5872.55

Step-by-step explanation:

According to the scenario, computation of the given data are as follow:-

At the retirement time required amount of money

Present value=PMT × 1 - (1 + rate) - time period ÷ rate

=$17000 × 1 - ( 1 + 0.10) -19 ÷ 0.10

=$17000 × 1 - (1.10) - 19 ÷ 0.10

=$17000 × 1 - 0.16351 ÷ 0.10

=$17000 × 0.83649 ÷ 0.10

=$17000 × 8.3649

= $142,203.3

Now Pre retirement amount of money:-

Future value = $142,203.3

Annual contribution PMT = future value × rate ÷ (1 + rate) time period - 1

= $142203.3 × 0.08 ÷ (1 + 0.08) 14 - 1

= $11376.264 ÷ (2.937194 - 1)

= $11376.264 ÷ 1.937194

= $5872.55

According to the analysis, annual contribution to the retirement fund is $5872.55

We simply applied the above formulas