Question

 

​(Compound

interest with​ non-annual

periods​)

You just received a bonus of

​$2,000.

a.  Calculate the future value of

​$2,000​,

given that it will be held in the bank for

8

years and earn an annual interest rate of

6

percent.b.  Recalculate part

​(a​)

using a compounding period that is​ (1) semiannual and​ (2) bimonthly. c.  Recalculate parts

​(a​)

and

​(b​)

using an annual interest rate of

12

percent.

d.  Recalculate part

​(a​)

using a time horizon of

16

years at an annual interest rate of

6

percent.e.  What conclusions can you draw when you compare the answers in parts

​(c​)

and

​(d​)

with the answers in parts

​(a​)

and

​(b​)?

a.  What is the future value of

​$2,000

in a bank account for

8

years at an annual interest rate of

6

​percent?

​$nothing  

​(Round to the nearest​ cent.)

Answer 1

a) For 8 years with interest rate 6%

FVn = PV(1+r)n

= 2000(1+6/100)8

  =2000(1+0.06)8

= 2000(1.06)8

=2000*1.593

=3186

b) Semi annually with interest rate 6%

FVn=PV(1+r)n

=2000(1+6/100)2

=2000(1+0.0⁶⁾²

=2000(1.06)2

=2000*1.1236

=2247.2

Biomonthly with interest rate 6%

FVn=PV(1+r)n

=2000(1+6/100)12

=2000(1+0.06)12

=2000(1.06)12

=2000*2.012

=4024.39

c) For 8 years with annual interest rate 12%

FVn=PV(1+r)n

=2000(1+12/100)8

=2000(1+0.12)8

=2000(1.12)8

=2000*2.475

=4951.92

Semi annually with interest rate or percentage

FVn=PV(1+r)n

=2000(1+6/100)2

=2000(1+0.06)2

=2000(1.06)2

=2000*1.1236

=2247.2

Biomonthly with interest rate 12%

FVn=PV(1+r)n

=2000(1+12/100)12

=2000(1+0.12)12

=2000(1.12)12

=2000*3.895

=7791.95

d) For 16 years with interest rate 6%

FVn=PV(1+r)n

= 2000(1+6/100)16

=2000(1+0.06)16

=2000(1.06)16

=2000*2.540

=5080.70

e) By comparing the answers of a and b with c and d it gives a conclusion that changes in the rate of interest and value of n may create a change in the future value of the given amount.