Question

​(Related to Checkpoint​ 5.2)  

​(Compound

interest with​ non-annual

periods​)

You just received a bonus of

​$3,000.

a.  Calculate the future value of

​$3,000​,

given that it will be held in the bank for

5

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

10

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

​$3,000

in a bank account for

5

years at an annual interest rate of

6

​percent?

​$nothing  

​(Round to the nearest​ cent.)

Answer 1

a)
FV = PV * (1+r)^n
= $3,000 * (1 + 6%)^5
= $4,014.68

Future value = $4,014.68

b)
Semiannual compounding:

FV = PV * (1+r/n)^(n*t)
= $3,000 * (1 + 6% / 2)^(5*2)
= $4,031.75

Future value = $4,031.75

bimonthly compounding:

FV = PV * (1+r/n)^(n*t)
= $3,000 * (1 + 6% / 6)^(6*5)
= $4,043.55

Future value = $4,043.55

c)
FV = PV * (1+r)^n
= $3,000 * (1 + 12%)^5
= $5,287.03

Future value = $5,287.03

Semiannual compounding:

FV = PV * (1+r/n)^(n*t)
= $3,000 * (1 + 12% / 2)^(5*2)
= $5,372.54

Future value = $5,372.54

bimonthly compounding:

FV = PV * (1+r/n)^(n*t)
= $3,000 * (1 + 12% / 6)^(6*5)
= $5,434.08

Future value = $5,434.08

d)
FV = PV * (1+r)^n
= $3,000 * (1 + 6%)^10
= $5,372.54

Future value = $5,372.54