Question

Fund A accumulates at an effective annual rate of 6% and Fund B accumulates at an effective annual rate of 8%. At the end of 20 years from now the total accumulated value of the two funds is $2,000. At the end of 10 years from now the amount in fund B is twice as large as the amount in Fund A. What is the total accumulated value of the two funds at the end of five years from now.

Answer 1

HI

Lets say present value of Fund A =A and present value of fund B = B

rate of fund A = 6% and rate of fund B = 8%

after 20 total value = $2,000

so

A*(1+6%)^20 +B*(1+8%)^20 = 2000

A*1.06^20 +B*(1.08)^20 =2000

and after 10 years fund B will be double of fund A

B*(1.08)^10 = 2*A*(1.06)^10

B = 2A*(1.06)^10/ 1.08^10

putting value of B in above equation

A*1.06^20 +2A*1.08^20*1.06^10/1.08^10 = 2000

3.21A + 7.73A =2000

A = 182.82

and B =2*182.82*1.06^10/1.08^10

B = 303.30

so total value of fund after years 5

=182.82*(1.06)^5 + 303.30*(1.08)^5 = $690.30

Thanks