Question

Mary is 30 years old and has $ 20,000 in her investment account equally spread in two funds and plans to add additional $ 2000 in each fund. ( 10 % of this grade)
Fund A :
Current amount : $ 10,000
Historical performance , 10 year average : 6.5 %
$2000 added ever year
Fund B :
Current amount : $ 10,000
Historical performance , 10 year average : 5 .5 %
$2000 added ever year
Calculate ( using 10 year average performance) amount in each fund, and total portfolio at      end of 10 years, 20 years and 30 years

Answer 1

Value of Portfolio at the end of 10 years

Fund A = Value of Current Amount $10000 after 10 years + Value of Annual Investment of $2000 for 10 years

Value of Current Amount $10000 after 10 years = 10000(1+r)n

= 10000(1+.065)10

10000*1.8771 = 18771

   

Value of Annual Investment of $2000 for 10 years = Annual Investment * ((1+r)n-1)/r)

= 2000*((1+.065)10-1)/.065)

= 2000*13.4944

= 26988.85

Total amount of Fund A = 18771+26988.85 = 45759.85

Fund B = Value of Current Amount $10000 after 10 years + Value of Annual Investment of $2000 for 10 years

Value of Current Amount $10000 after 10 years = 10000(1+r)n

= 10000(1+.055)10

10000*1.7081 = 17081

Value of Annual Investment of $2000 for 10 years = Annual Investment * ((1+r)n-1)/r)

= 2000*((1+.055)10-1)/.055)

= 2000*12.8754

= 25750.80

Total amount of Fund B = 17081+25750.80 = 42831.80

VALUE OF PORTFOLIO = 45759.85 + 42831.80 = 88591.65

Value of Portfolio at the end of 20 years

Fund A = Value of Current Amount $10000 after 20 years + Value of Annual Investment of $2000 for 20 years

Value of Current Amount $10000 after 10 years = 10000(1+r)n

= 10000(1+.065)20

10000*3.5236 = 35236

   

Value of Annual Investment of $2000 for 20 years = Annual Investment * ((1+r)n-1)/r)

= 2000*((1+.065)20-1)/.065)

= 2000*38.8253

= 77650.60

  Total amount of Fund A = 35236+77650.60 = 112886.60

Fund B = Value of Current Amount $10000 after 20 years + Value of Annual Investment of $2000 for 20 years

Value of Current Amount $10000 after 10 years = 10000(1+r)n

= 10000(1+.055)20

10000*2.9178 = 29178

Value of Annual Investment of $2000 for 20 years = Annual Investment * ((1+r)n-1)/r)

= 2000*((1+.055)20-1)/.055)

= 2000*34.8683

= 69736.60

  Total amount of Fund B = 29178+69736.60 = 98914.60

VALUE OF PORTFOLIO = 112866.60+ 98914.60 = 211781.20

Value of Portfolio at the end of 30 years

Fund A = Value of Current Amount $10000 after 30 years + Value of Annual Investment of $2000 for 30 years

Value of Current Amount $10000 after 10 years = 10000(1+r)n

= 10000(1+.065)30

10000*6.6144= 66144

   

Value of Annual Investment of $2000 for 10 years = Annual Investment * ((1+r)n-1)/r)

= 2000*((1+.065)30-1)/.065)

= 2000*86.3749

= 172749.80

  Total amount of Fund A = 66144+172749.80 = 238893.80

Fund B = Value of Current Amount $10000 after 30 years + Value of Annual Investment of $2000 for 30 years

Value of Current Amount $10000 after 10 years = 10000(1+r)n

= 10000(1+.055)30

10000*4.9840 = 49840

Value of Annual Investment of $2000 for 10 years = Annual Investment * ((1+r)n-1)/r)

= 2000*((1+.055)30-1)/.055)

= 2000*72.4355

= 144871

  Total amount of Fund B = 49840+144871= 194711

VALUE OF PORTFOLIO = 238893.80+ 194711 = 433604.80

NOTE: The solution has been framed on the assumption that the $2000 is invested at the end of