Question

What is the discounted value of

​$844

paid at the end of every

three months

for

10

years if interest is

9 %

per annum compounded monthly..

Please provide the appropriate formula and show work. Please do not use excel.

Answer 1

$ 22,043.19

Step-1:Calculation of equivalent 3 month's interest rate
(1+i)^n	=	(1+i)^n		Where,
(1+0.0075)^3	=	(1+i)^1		Monthly interest rate	=	9%/12
1.022669	=	1+i			=	0.0075
0.022669	=	i
thus,
Equivalent 3-months interest rate	=	0.02266917
Step-2:Calculation of discounted value
Discounted Value	=	Cash Flow every 3 months	*	Present Value of annuity of 1
	=	$       844.00	*	26.11753
	=	$ 22,043.19
Working:
Present Value of annuity of 1	=	(1-(1+i)^-n)/i	Where,
	=	26.1175264		i	=	0.022669
				n	=	40