Question

Find the PV of an annuity payable in arrears of $1,000 p.a. payable quarterly for 25 years at an

effective rate of interest of 6% p.a

Answer 1

Step-1:Calculation of nominal rate of return
Effective rate of interest		=	((1+(i/n))^n)-1			Where,
0.06		=	((1+(i/4))^4)-1			i	=	?
1.06		=	(1+(i/4))^4			n	=	4
1.06	^ (1/4)	=	1+(i/4)
1.014674		=	1+(i/4)
0.014674		=	i/4
0.058695		=	i
So,
Nominal rate of return		=	5.87%
Step-2:Calculation of PV of annuity payable in arrears
PV of annuity		=	Annuity	*	Present value of annuity of 1
		=	$       250.00	*	52.26996
		=	$ 13,067.49
Working;
Present value of annuity of 1		=	(1-(1+i)^-n)/i		Where,
		=	52.2699612		i	=	5.87%	/	4	=	0.014674
					n	=	25	*	4	=	100
Quarterly annuity		=	$   1,000.00	/	4
		=	$       250.00