Sam retires today at the age of 61 and invests his life savings into an account...

Sam retires today at the age of 61 and invests his life savings into an account that is guaranteed to earn 3.83% per year. Sam expects to live to the age of 92, withdraw $0.103mln from the account at the end of each year, and leave his heirs $1.726mln (this amount will be the account balance at the time of his death). How much is Sam putting in the account today, in $ million? Round to the nearest $0.001 million. E.g., if your answer is $1,234,758, record it as 1.235.

Expert Solution

	No of years in consideration =(92-61)=31
	We have to find the PV of Annuity and PV of
	$1.726 M as on today.
	Formula for present value of an anuuity = PV= A [ {(1+k)ⁿ-1}/k(1+k)ⁿ]
	PV = Present value of Loan =
	A = periodical Yearly payment =$0.103 M
	k=interest rate=3.83% per year
	n=periods=31 years
	PV =0.103[(1.0383^31-1)/(3.83%)(1.0383)^31]
	PV =$1.8505 M
b	So PV of Annuity =$1.8505 Million

	Now let us find the PV of $1.726 Million which
	will accumulate after 31 years from today.
	Interest rate =3.83% pa
	PV =$1.726 Million/1.0383^31
a	PV =$1.726 Million/3.2063319 =	$ 0.5383	Million

	So PV of the Annuity+PV of Account Balance=a+b=	$ 2.38880	Million

jeff jeffy answered 1 year ago

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