Tuitorial - Time Value Of Money ( Discussion Only )



Future Value Of Present Sum
FV = PV x ( 1 + r )n

Notation
PV = present value is the value at time = 0
FV = future value is the value at time = n
r = rate at which the mount will be compounded each period
n  = number of periods

Questions : 
  1. Find out the future value at the end of 14 year of RM 1,000 invested today at an interest rate of 14%
  2. Find out the future value at the end of 6 year of RM 1,000 invested today at an interest rate of 13%
  3. Find out the future value at the end of 10 year of RM 15,000 invested today at an interest rate of 8%
  4. Find out the future value at the end of 8 year of RM 9,000 invested today at an interest rate of 6%
  5. Find out the future value at the end of 4 year of RM 2,000 invested today at an interest rate of 4%
Answer :

Find out the future value at the end of 14 year of RM 1,000 invested today at an interest rate of 14%
 FV = PV x ( 1 + r )n
      = RM 1,000 x ( 1 + 14%) 14
      = RM 1,000 x ( 1 + 0.14 ) 14
      = RM 1,000 x ( 1.14 ) 14
      = RM 1,000 x 6.26135
      = RM 6,261.35


Find out the future value at the end of 6 year of RM 1,000 invested today at an interest rate of 13%
 FV = PV x ( 1 + r )n
      = RM 1,000 x ( 1 + 13%) 6
      = RM 1,000 x ( 1 + 0.13 ) 6
      = RM 1,000 x ( 1.13 ) 6
      = RM 1,000 x2.08195
      = RM 2,081.95


 Find out the future value at the end of 10 year of RM 15,000 invested today at an interest rate of 8%
 FV = PV x ( 1 + r )n
      = RM 15,000 x ( 1 + 8%) 10
      = RM 15,000 x ( 1 + 0.08 ) 10
      = RM 15,000 x ( 1.08 ) 10
      = RM 15,000 x 2.15892
      = RM32,383.87

 Find out the future value at the end of 8 year of RM 9,000 invested today at an interest rate of 6%
 FV = PV x ( 1 + r )n
      = RM 9,000 x ( 1 + 6%) 8
      = RM 9,000 x ( 1 + 0.06 ) 8
      = RM 9,000 x ( 1.06 ) 8
      = RM 9,000 x1.59385
      = RM 14,344.63


 Find out the future value at the end of 4 year of RM 2,000 invested today at an interest rate of 4%
 FV = PV x ( 1 + r )n
      = RM 2,000 x ( 1 + 4%) 4
      = RM 2,000 x ( 1 + 0.04 ) 4
      = RM 2,000 x ( 1.04 ) 4
      = RM 2,000 x 1.1698
      = RM 2,339.72

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Present Value of Future Sum
PV = FV / ( 1 + r ) n

Notation
PV = present value is the value at time = 0
FV = future value is the value at time = n
r = rate at which the mount will be compounded each period
n  = number of periods

Questions :
  1. Find out the present value of RM 200 for 3 years if the interest rate is 9%
  2. Find out the present value of RM 100 for 1 years if the interest rate is 2%
  3. Find out the present value of RM 3,000 for 3 years if the interest rate is 1% 
  4. Find out the present value of RM 1,500 for 2 years if the interest rate is 1.5%
  5. Find out the present value of RM 6,500 for 1 years if the interest rate is 2.5% 
Answer :

Find out the present value of RM 200 for 3 years if the interest rate is 9%
1. PV = FV / ( 1 + r ) n
           = RM 200 / ( 1 + 9% ) 3
           =  RM 200 / ( 1.09 ) 3
           = RM 200 / 1.295
           =  RM 154.44

Find out the present value of RM 100 for 1 years if the interest rate is 2%
2. PV = FV / ( 1 + r ) n
           = RM 100 / ( 1 + 2% )  1
           =  RM 100 / ( 1.02 ) 1
           = RM 100 / 1.02
           =  RM 98.04

Find out the present value of RM 3,000 for 3 years if the interest rate is 1% 
3. PV = FV / ( 1 + r ) n
           = RM 3,000 / ( 1 + 1% )  3
           =  RM 3,000 / ( 1.01 ) 3
           = RM 3,000 / 1.03
           =  RM 2,911.77

 Find out the present value of RM 1,500 for 2 years if the interest rate is 1.5%
4. PV = FV / ( 1 + r ) n
           = RM 1,500 / ( 1 + 1.5% )  2
           =  RM 1,500 / ( 1.015 ) 2
           = RM 1,500 / 1.030225
           =  RM1,455.99

 Find out the present value of RM 6,500 for 1 years if the interest rate is 2.5%
5.  PV = FV / ( 1 + r ) n
           = RM 6,500 / ( 1 + 2.5% )  1
           =  RM 6,500 / ( 1.025 ) 1
           = RM 6,500 / 1.025
           =  RM 6,341.46

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