Question

FUTURE VALUE OF AN ANNUITY Find the future values of these ordinary annuities. Compounding occurs once a year. Round your answers to the nearest cent. a. $200 per year for 6 years at 6%. $ b. $100 per year for 3 years at 3%. C. $1,000 per year for 12 years at 0%. सी Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent. d. $200 per year for 6 years at 6%. e. $100 per year for 3 years at 3%. f. $1,000 per year for 12 years at 0%. $

Answer 1

We are given the following information:

Particular	a)	b)	c)
PMT	$                  200.00	100	1000
r	6.00%	3.00%	0%
n	6	3	12

We need to solve the following equation to arrive at the required FV

a)

(1+r)" - 1 FV = PMT X- FV = 200 x (1 +0.06)6 – 1 0.06 FV = 1395.06

So the FV is $1395.06

b)

(1+r)" - 1 FV = PMT X- FV = 100 x (1 +0.03)3 – 1 0.03 FV =309.09

c)

FV = PMT X (1+r)" – 1 FV = 1000 X (1+0)12 - 1 FV =12000

For annuity due, the first payment is made at time 0 instead of time 1 and therefore the payments are compounded for 1 extra period

d)

FV = PMTX (1+r)" -1 x (1+r) (1 +0.06)6 - 1 FV = 200 x = x (1 + 0.06) 0.06 FV = 1478.76

e)

FV = PMT X (1+r)" - 1 X (1+r) (1+0.03)3 – 1 FV = 100 x = x (1 + 0.03) 0.03 FV = 318.36

f)

FV = PMT X (1+r)"-1. x (1+r) FV = PMT (1+0)12 - 1 - X (1+0) FV = 12000