(a) An annuity is defined as a series of payments of a fixed amount for a specif

Question

(a) An annuity is defined as a series of payments of a fixed amount for a specific number of periods. Thus, $100 a year for 10 years is an annuity, but $100 in Year 1, $200 in Year 2, and $400 in Years 3 through 10 does not constitute an annuity. However, the entire series does contain an annuity. Is this statement true or false? And Why?

                        (b) Your parents will retire in 18 years. They currently have $250,000, and they think they will need $1 million at retirement. What annual interest rate must they earn to reach their goal, assuming they don’t save any additional funds?

Explanation / Answer

a) Yes the statement is true. The second series of payments are variable is called a variable Annuity. The first series of payments where amount paid per year is fixed is called a fixed Annuity while second series where yearly payments are variable is called a variable Annuity is also a type of Annuity, therefore second series is also an Annuity.

b) $250,000*(1+r)^18=1000000, where r is the interest rate they earn , the present amount is compounded annually at this rate of interest r for 18 yrs to reach the goal of having a $ 1 million.

Rearrange above equation, (1+r)^18=1000000/250,000 =4

take 1/18th power on both sides => 1+r=4^(1/18)=1.0800=>r=1.08-1=.08 => r=8% therefore they must earn 8% annualy as a rate of interest to reach their goal.

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