Question

You just received a bonus of $4,000.

a. Calculate the future value of $4,000​ given that it will be held in the bank for 5 years and earn an annual interest rate of 7 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 14 percent.

d. Recalculate part (a​) using a time horizon of 10 years at an annual interest rate of 7 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​)?

Answer 1

Future value = PV * ((1+ interest rate * number of years)

a) Future value = 4000*((1+0.07*5)

= $5,400

b) For compounding period semiannual,

Future value = PV * (1+r/2)^n*2

= 4000 * (1+0.035)^10

= $5462.39

Compounding period bimonthly

Future value = 4000 * (1+0.07/24)^5*24

= $5673.38

c) Using annual interest rate of 14%:

Future value with simple interest = 4000*(1+(0.14*5)

= $6800

Future value with semi annual compunding = 4000 * (1+0.14/2)^5*2

= $7868.60

Future value with bimonthly compunding = 4000 * (1+0.14/24)^5*24)

= $8038.65

d) Future value with n = 10 years and i = 7%

Future value simple interest = 4000 * (1+(0.07*10))

= $6800

e) With an increase in the compunding, the future value increases. In case of simple interest, both interest and timw period have the same effect as the future value in c and d are the same. In case of compounding, with an increase in the innterest rate, the future value also increases.