Question

Compute the amount that a $20,000 investment today would

accumulate to at the end of 10 years, 8% interest compounded quarterly.

$ __________

   Part (b) Fran wants to retire at the end of this year (2020). Her

life expectancy is 35 years from her retirement. She has

come to you, her CPA, to learn how much she should deposit

on December 31, 2020 to be able to withdraw $100,000 at the

end of each year for the next 35 years, assuming the amount

on deposit will earn 8% interest annually.

$ __________

Answer 1

	Question 1	Computation of future value of a sum invested today
		Future value= Present value*(1+ interest rate)^ no of period compounded
		Since the it is quarterly compounding the interest rate would be divided by 4 and period would be multiplied by 4
		10 Years= 40 Compounded period
		8%=2% as it is compounded quarter
		Future value=	20,000	(1+2%)^40
		Future value=	20,000	2.208039664
	Final answer	Future value=	44,161
	Question 2 I.e.. part b)	Computation of amount to be invested today
		The amount to be invested today is nothing but a present value of all the amount received over period of 35 years
		so the calculation would be as follows
	Present value of annuity=	PMT*	(1-1/(1+i^n)
			r
	PMT =	Amount received every year (i.e. $ 100,000)
	r	Rate of interest (i.e. 8%)
	n	No of period (i.e. 35 years)
	Present value of annuity=	100000 *	1-(1/(1+8%)^35)
			8%
	Present value of annuity=	100000 *	93%
			8%
	Present value of annuity=	100000 *	11.65
Final answer	Present value of annuity=	1,165,457