Question

Future value of retirement accounts. 20k to start, 5k additional each year for 35 years. (age 30-65).

Account 1: fee of .0117; return rate of .0442 annually.
Account 2: fee of .0004; return rate of .0834 annually.

FV_n = [C(1 – TC) * (1+r)ⁿ] + PMT(1-TC)[(1+r)n – 1/r]

FV₃₅ = [20,000(1-.0117) * (1+.0442)³⁵ + 5000(1-.0117) [(1+.0442)³⁵ – 1 / .0442) =

FV₃₅ = [20,000(1-.0004) * (1+.00834)³⁵ + 5000(1-.0004) [(1+.0834)³⁵ – 1 / .0834) =

Answer 1

1.

1.0442^35= 4.54

1-0.117= 0.9883

Here, FV= ((20000*0.9883)*1.0442^35)+ 5000(0.9883)((1.0442^35)-1)/0.0442

FV= 19776*4.45)+ 4941.50(4.54-1)/0.0442

= 89814.80+ 4941.50* 3.54/0.0442

=89814.80+396203.61

=$486,018.41

2.

1.0834^35= 16.50

1-0.004= 0.9996

Here, FV= ((20000*0.9996)*1.0834^35)+ 5000(0.99)((1.0834^35)-1)/0.0834

FV= (19992*16.50)+ 4998(16.50-1)/0.0834

= 32996.07+ 4998*15.50/0.0834

=329963.07+929169.88

=$1,259,132.95