Question

1 ) Tim plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If tim can earn 12 percent on his contributions, how much will he have at the end of the twentieth year?

2) The present value of an ordinary annuity of $2,350 each year for eight years, assuming an opportunity cost of 11 percent, is ?

3) The future value of an ordinary annuity of $1,000 each year for 10 years, deposited at 3 percent, is ?

4) Dominique  will receive $12,000 per year for the next 10 years as royalty for her work on a finance book. What is the present value of her royalty income if the opportunity cost is 12 percent?

Answer 1

Solution 1
	FV of annuity
	P = PMT x ((((1 + r) ^ n) - 1) / r)
	Where:
	P = the future value of an annuity stream	To be computed
	PMT = the dollar amount of each annuity payment	$                2,000
	r = the effective interest rate (also known as the discount rate)	12%
	n = the number of periods in which payments will be made	20
	FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / r)
	FV of annuity=	2000* ((((1 + 12%) ^ 20) - 1) / 12%)
	FV of annuity=	$      144,104.88
Solution 2
	PV of annuity
	P = PMT x (((1-(1 + r) ^- n)) / r)
	Where:
	P = the present value of an annuity stream	To be computed
	PMT = the dollar amount of each annuity payment	$                2,350
	r = the effective interest rate (also known as the discount rate)	11%
	n = the number of periods in which payments will be made	8
	PV of annuity=	PMT x (((1-(1 + r) ^- n)) / r)
	PV of annuity=	2350* (((1-(1 + 11%) ^- 8)) / 11%)
	PV of annuity=	$        12,093.39
Solution 3
	FV of annuity
	P = PMT x ((((1 + r) ^ n) - 1) / r)
	Where:
	P = the future value of an annuity stream	To be computed
	PMT = the dollar amount of each annuity payment	$                1,000
	r = the effective interest rate (also known as the discount rate)	3%
	n = the number of periods in which payments will be made	10
	FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / r)
	FV of annuity=	1000* ((((1 + 3%) ^ 10) - 1) / 3%)
	FV of annuity=	$        11,463.88
Solution 4
	PV of annuity
	P = PMT x (((1-(1 + r) ^- n)) / r)
	Where:
	P = the present value of an annuity stream	To be computed
	PMT = the dollar amount of each annuity payment	$              12,000
	r = the effective interest rate (also known as the discount rate)	12%
	n = the number of periods in which payments will be made	10
	PV of annuity=	PMT x (((1-(1 + r) ^- n)) / r)
	PV of annuity=	12000* (((1-(1 + 12%) ^- 10)) / 12%)
	PV of annuity=	$        67,802.68