Question

$100 S $315.25 FVAN PMT 0.050 Future Value of Annuity 500 400 300 200 100 0 1 2 Period Int 5 10 5 PMT = 100 200 400 N 3

Answer 1

Answer 1

n=10 years, PMT = $200, r= 6%

From FV = PMT *((1+r)^n-1)/r

we get, FV = 200*((1+6%)^10-1)/6%

=200*(1.06^10-1)/0.06

=200*(1.791-1)/0.06

=200*0.791/0..06

=$2636.16

Hence FV = $2636.16 i. e option c

Answer 2

n=3 yrs, PMT = $100, r= 5%

From FV = PMT *((1+r)^n-1)/r

we get, FV = 100*((1+5%)^3-1)/5%

=100*(1.05^3-1)/0.05

=100*(1.1576-1)/0.05

=100*0.1576/0.05

=$315.25 (this FV will be used as reference for answer 2,3 and 4)

Now if interest rate doubles to 10%

FV = 100*((1+10%)^3-1)/10%

=100*(1.10^3-1)/0.10

=100*(1.331-1)/0.10

=100*0.331/0.10

=$331

Hence FV increases but by less than double, hence option a is correct

Answer 3

Now if payment doubles to 200

FV =200*((1+5%)^3-1)/5%

=200*(1.05^3-1)/0.05

=200*(1.1576-1)/0.05

=200*0.1576/0.05

=$630.5

Hence FV increases exactly by double, hence option b is correct

Answer 4

Now if n=6 yrs

FV = 100*((1+5%)^6-1)/5%

=100*(1.05^6-1)/0.05

=100*(1.34-1)/0.05

=100*0.34/0.05

=$680.19

Hence FV increases by more than double hence option c is correct