Question

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 6 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 12 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​)?

Answer 1

a. PV =3000
Rate =6%
Number of years =6
FV=PV*(1+r)^n =3000*(1+6%)^6 =4255.56

b. 1. Semi annual
Number of Periods =6*2 =12
Rate semi annually =6%/2 =3%
FV=PV*(1+r)^n =3000*(1+3%)^12 =4277.28

2. Bimonthly
Number of Periods =6*26 =156
Rate semi annually =6%/26
FV=PV*(1+r)^n =3000*(1+6%/26)^156 =4298.21

c. Rate =12%
Number of years =6
FV=PV*(1+r)^n =3000*(1+12%)^6 =5921.47

Semi annual
Number of Periods =6*2 =12
Rate semi annually =12%/2 =6%
FV=PV*(1+r)^n =3000*(1+6%)^12 =6036.59

Bimonthly
Number of Periods =6*26 =156
Rate semi annually =12%/26
FV=PV*(1+r)^n =3000*(1+12%/26)^156 =6153.10

d) Rate =6%
Number of years =12
FV=PV*(1+r)^n =3000*(1+6%)^12 =6036.59

e) Higher the rate, higher is the FV for same maturity.
Higher the number of years , higher is the FV for same rate of interest.