Question

you. 6.27 How much must you deposit each year into your re- tirement account starting now and continuing

Answer 1

Ans a) Value at 30 year should be = $80000/interest rate

= $80000/.1

= $800,000

Value at 10 year should be = value at 30 year/(1 + interest rate)^20

= $800,000/(1.1)^20

= $118,914.9

we will use formula of annuity due to this question:

Future value of annuity due = (1 + r) * P ((1+r)^n - 1)/r

Future value of annuity due = $118,914.9

r = 10%

n = 10

118,914.9 = 1.1 * P * ((1.1)^10 - 1)/.1

P = $6783.06

Ans b) similarly we will find for section b

Value at 30 year should be = $80000/interest rate

= $80000/.04

= $2,000,000

Value at 10 year should be = value at 30 year/(1 + interest rate)^20

= $2,000,000/(1.04)^20

= $912,773.90

we will use formula of annuity due to this question:

Future value of annuity due = (1 + r) * P ((1+r)^n - 1)/r

Future value of annuity due = $912,773.90

r = 4%

n = 10

118,914.9 = 1.04 * P * ((1.04)^10 - 1)/.04

P = $73,101.73

In conservative approach one has to deposit almost 11 times than the aggressive approach to finance the retirement fund.