Question

5) When you retire you want to have enough saved in an account that pays 5% to meet your expenses for the next 20 years. You want to be able to withdraw $50,000 at the end of the first year, and after that, the withdrawals will be reduced by 2,000 per year up to the 20th year. How much should you have in the account when you retire?

Answer 1

As per the information provided in the question

The interest rate of the saving account (i) =5%

The withdrawal period (N) =20 years

After retirement the first withdraw is $50000 at the end of 1^st year and there after the annual withdraw decreases by $2000 per year

So A1 =$50000

G=$2000

A = A1 – G(A/G,i,N)

A = $50000 – $2000(A/G,5%,20)

A = $50000 – $2000(7.9030) = $50000 -$15806 =$34,194

The present worth of the annual withdraw (P) = A(P/A,i,N) = $34,194(P/A,5%,20)

= $34,194(P/A,5%,20) = = $34,194(12.4622) = $426132.4668    or   Approx $426132.47

The account should have amount at the time of retirement is $426132.47