Annuity and compounding

by

 

Part A: 

By the end of this year you would be 35 years old and you want to plan for your retirement. You wish to retire at the age of 65 and you expect to live 20 years after retirement. Upon retirement you wish to have an annual sum of $50,000 to supplement your social security benefits. Therefore, you opened now  your retirement account with 7% annual interest rate. At retirement you liquidate your  account and use the funds to buy an  investment grade bond which makes $50,000 annual coupon payments based on a 6 % coupon rate, throughout your retirement years. 

  1. How much will the face value of the bond that you will be investing?
  2. Please calculate the monthly payment in your retirement account in order to be able to achieve the plan mentioned above? 
  3. How much will your inheritors receive? 

Now lets extend the problem so that you protect yourself against inflation.

Part B: 

Suppose you think if you were to retire right now you would have needed $50,000 each year to supplement your social security and maintain your desired lifestyle. But because there is on average 3% annual inflation, when you retire in 30 years from now you need more than $50,000 per year to maintain the lifestyle you like. 

  1. How much will be equivalent to $50,000 at the retirement time when adjusted for inflation?
  2. How much will be the face value of the bond that yields the equivalent of $50,000, found in #4 of Part B in coupon payment?
  3. How much annual payment in the retirement account is needed to accumulate the amount needed to purchase the bond when retiring? 
  4. What is the purchase power of the amount that will be received by your inheritors, measured in the current value of $ at the time of opening the retirement account? 

(Hint: First calculate what future amount in 30 years, which is equivalent to $50,000 of now and then solve the rest of the problem).

Provide your explanations and definitions in detail and be precise. Comment on your findings. Provide references for content when necessary. Provide your work in detail and explain in your own words. Support your statements with peer-reviewed in-text citation(s) and reference(s).