Question

e. What is an annuity​ due? How does this differ from an ordinary​ annuity?

Answer 1

Annuity is the fixed amount of money at periodical interval.
There are two types of annuity:
(a)	Annuity due
(b)	Ordinary annuity
(a)	Annuity due
In case of annuity due, amount is received or invested at the beginning of period.
For example, $ 1 is received or invested at the beginning of each year for 5 years at 10% compounded annually.
In such case,
Future value of annuity	=	((((1+i)^n)-1)/i)*(1+i)			where,
	=	((((1+0.10)^5)-1)/0.10)*(1+0.10)			i	10%
	=	$ 6.71561			n	5
or,
Present value of annuity	=	((1-(1+i)^-n)/i)*(1+i)			where,
	=	((1-(1+0.10)^-5)/0.10)*(1+0.10)			i	10%
	=	$ 4.16987			n	5
(b)	Ordinary annuity
In case of ordinary annuity, amount is received or invested at the end of period.
For example, $ 1 is received or invested at the end of each year for 5 years at 10% compounded annually.
In such case,
Future value of annuity	=	(((1+i)^n)-1)/i			where,
	=	(((1+0.10)^5)-1)/0.10			i	10%
	=	$ 6.10510			n	5
or,
Present value of annuity	=	(1-(1+i)^-n)/i			where,
	=	(1-(1+0.10)^-5)/0.10			i	10%
	=	$ 3.79079			n	5