Petter is planning his retirement. He want to receive $100,000 10 years from today and a...

Petter is planning his retirement. He want to receive $100,000 10 years from today and a retirement annuity of $80,000 per year for 20 years with the first payment 20 years from today. To pay for this, peter will make 3 annual payments of $X per year beginning today and 2 annual payments of $X per year with the first payment 7 years from today. With an interest rate of 8%, what is the value for X Type?

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Expert Solution

ie.PV of a single sum of $ 100000 at end of 10 yrs.+PV of annuity of $ 20000 /yr. for 20 yrs.from yr.20 SHOULD Equal

PV of sum of ($ x, pmt. Today, end of next yr., end of yr. 2 , end of yr. 7 & end of yr. 8)

all at 8% p.a. interest

(100000/1.08^10)+(80000*(1-1.08^-20)/0.08*1.08/1.08^20)=x+(x/1.08^1)+(x/1.08^2)+(x/1.08^7)+(x/1.08^8)

Solving for x, we get tha value of X as

58437.80

jeff jeffy answered 1 year ago

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