Question

Compute the future values of the following annuities first assuming that payments are made on the last day of the period and then assuming payments are made on the first day of the period: (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Payment	Years	Interest Rate (Annual)	Future Value (Payment made on last day of period)	Future Value (Payment made on first day of period)
$      183	13	12%	$	$
5,155	8	11
75,084	5	13
167,932	9	4

Answer 1

Payment	Years	Interest rate			Future Value (Payment made on last day of period)		Future Value (Payment made on first day of period)
		(Annual)
$ 183	13	12%			$ 5,129.33			$          5,744.85
5,155	8	11			61,135.38			67,860.28
75,084	5	13			4,86,564.64			5,49,818.04
1,67,932	9	4			17,77,189.98			18,48,277.58
Workings:
There are two types of annuity-(a) Annuity due and (b) Ordinary Annuity
When payments are made at the beginning of period, is termed as annuity due and on the other hand if at the end of period is know as ordinary annuity.
Future Value of Ordinary Annuity				=	(((1+i)^n)-1)/i		Where,
							i	Interest rate
							n	Life in years
Future Value of annuity due				=	((((1+i)^n)-1)/i)*(1+i)
Working:
Future Value of annuity due of 1 in case of:
$ 183		((((1+0.12)^13)-1)/0.12)*(1+0.12)			31.3926
5,155		((((1+0.11)^8)-1)/0.11)*(1+0.11)			13.1640
75,084		((((1+0.13)^5)-1)/0.13)*(1+0.13)			7.3227
1,67,932		((((1+0.04)^9)-1)/0.04)*(1+0.04)			11.0061
Future Value of annuity of:
$ 183			$                     183	x	31.3926	$      5,744.85
5,155			$                 5,155	x	13.1640	67,860.28
75,084			$               75,084	x	7.3227	5,49,818.04
1,67,932			$           1,67,932	x	11.0061	18,48,277.58
Future Value of ordinary annuity of 1 in case of:
$                 183		(((1+0.12)^13)-1)/0.12			28.0291
5,155		(((1+0.11)^8)-1)/0.11			11.8594
75,084		(((1+0.13)^5)-1)/0.13			6.4803
1,67,932		(((1+0.04)^9)-1)/0.04			10.5828
Future Value of annuity of:
$                 183			$                     183	x	28.0291	$      5,129.33
5,155			$                 5,155	x	11.8594	61,135.38
75,084			$               75,084	x	6.4803	4,86,564.64
1,67,932			$           1,67,932	x	10.5828	17,77,189.98