Question

Annuities: 4 questions

Q1: -PV: I save $200/year for 20 years at 5%. What is the present value of these savings?

Q2: -FV: I save $200/year for 20 years at 5%. How much will I have in 20 years?

Q3: -Payment: I want a $ 1 million in 25 years. I can earn 7% annually. How much do I need to save each month?

Q4: -Rate: I invest $250,000 and receive $20,000/year for next 20 years, what rate am I earning?

Answer 1

1)	Present value of saving	=	Annual saving	*	Present value of annuity of 1
		=	$                   200	*	12.46221
		=	$          2,492.44
	Working;
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.05)^-20)/0.05		i	5%
		=	12.46221034		n	20
2)	Future value of saving	=	Annual saving	*	Future value of annuity of 1
		=	$                   200	*	33.06595
		=	$          6,613.19
	Working;
	Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
		=	(((1+0.05)^20)-1)/0.05		i	5%
		=	33.0659541		n	20
3)	Monthly saving	=	Future value of monthly saving	/	Future value of annuity of 1
		=	$       10,00,000	/	810.0204
		=	$          1,234.54
	Working;
	Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
		=	(((1+0.005833)^300)-1)/0.005833		i	7%/12	=	0.005833
		=	810.0204039		n	25*12	=	300
4)	Interest rate	=	=rate(nper,pmt,pv)		Where,
		=	4.96%		nper	20
					pmt	$             20,000
					pv	$       -2,50,000