Question

Can you show me how to do this step by step? We are not allowed to use excel. Everything has to be done by hand or with a financial calculator

You are scheduled to receive annual payments of $10,000 for each of the next 25 years. Your discount rate is 8.5%. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year

Answer 1

Step-1:Present value of cash flow if payments are received at the beginning of period
Present value		=	Annual cash flow	*	Present value of annuity of 1
		=	$           10,000	*	11.104097
		=	$ 1,11,040.97
Working:
Present value of annuity of 1		=	((1-(1+i)^-n)/i)*(1+i)		Where,
		=	((1-(1+0.085)^-25)/0.085)*(1+0.085)		i	=	8.50%
		=	11.104097		n	=	25
Step-2:Present value of cash flow if payments are received at the end of period
Present value		=	Annual cash flow	*	Present value of annuity of 1
		=	$           10,000	*	10.23419078
		=	$ 1,02,341.91
Working:
Present value of annuity of 1		=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.085)^-25)/0.085		i	=	8.50%
		=	10.23419078		n	=	25
Step-3:Calculation of difference in present value
Difference in present value		=	$ 1,11,040.97	-	$ 1,02,341.91
		=	$       8,699.06