Question

Suppose you receive $100 at the end of each year for the next three years.

(a)If the interest rate is 9%, what is the present value (in $) of these cash flows?

Compute the PV of this annuity both as the sum of PV of each cash flow and using the annuity formula. (Round your answers to the nearest cent.)

using the sum of PV

$

using the annuity formula

$

(b)What is the future value (in $) of the payments in three years (on the date of the last payment)? (Round your answer to the nearest cent.)

$

Answer 1

a) PV using the sum PV is as follows:

Year	CF	Discount Factor		Discounted CF
1	$      100.00	1/(1+0.09)^1=	0.917431193	0.91743119266055*100=	$         91.74
2	$      100.00	1/(1+0.09)^2=	0.841679993	0.84167999326656*100=	$         84.17
3	$      100.00	1/(1+0.09)^3=	0.77218348	0.772183480061064*100=	$         77.22
				PV = Sum of all Discounted CF	$      253.13

PV using the annuity formula is calculated below

PV = PMT x 1-(1+r)-n PV = 100 1-(1 +0.09)-3 0.09 PV = 253.13

r = rate, n = time, PMT = annual payment of 100

b) FV of all the CFs on the date of last payment using the annuity formula is calculated as follows:

(1+r)" - 1 FV = PMTX FV = PMTX (1 +0.09) 3 - 1 0.09 FV = 327.81

FV of all the CFs on the date of last payment using the sum of FV is calculated as follows:

Year	CF	Compounding Factor		Compounded CF
1	$      100.00	(1+0.09)^(3-1)=	1.1881	1.1881*100=	$      118.81
2	$      100.00	(1+0.09)^(3-2)=	1.09	1.09*100=	$      109.00
3	$      100.00	(1+0.09)^(3-3)=	1	1*100=	$      100.00
				FV = Sum of all Compounded CF	$      327.81