Question

#5) Sasha has an investment worth 8,640 dollars. The investment will make a special payment of X to Sasha in 6 years from today. The investment also will make regular, fixed annual payments of 1,000 dollars to Sasha with the first of these payments made to Sasha later today and the last of these annual payments made to Sasha in 9 years from today. The expected return for the investment is 6.63 percent per year. What is X, the amount of the special payment that will be made to Sasha in 6 years?

Answer 1

X is $1,500.68

Working:

Investment amount is the present value of future cash flows.
Step-1:Calculation of present value of annual payments
Present value of annual cash flows	=	Annual cash flows	*	Present value of annuity of 1
	=	$       1,000	*	7.619032
	=	$ 7,619.03
Working:
Present value of annuity of 1	=	((1-(1+i)^-n)/i)*(1+i)		Where,
	=	((1-(1+0.0663)^-10)/0.0663)*(1+0.0663)		i	6.63%
	=	7.6190316		n	10
Step-2:Calculate the value of X
Cash flow 6 years from today(X)	=	Balance investment amount	*	(1+i)^n		Where,
	=	$ 1,020.97	*	(1+0.0663)^6		i	6.63%
	=	$ 1,020.97	*	1.469862		n	6
	=	$ 1,500.68
Working:
Total investment amount today		$ 8,640.00
Less:Present value of annual cash flow		$ 7,619.03
Balance investment amount		$ 1,020.97