Question

Derek currently has $12,018.00 in an account that pays 5.00%. He will withdraw $5,543.00 every other year beginning next year until he has taken 8.00 withdrawals. He will deposit $12018.0 every other year beginning two years from today until he has made 8.0 deposits. How much will be in the account 28.00 years from today?

Answer 1

Answer:

Beginning balance in the account = $12,018

Rate of interest = 5%

Withdrawal = $5,543 every other year beginning next year until 8 withdrawal

Deposit = $12,018 every other year beginning two years from now until 8 deposits

No of years of accumulated = 28 years

To calculate the balance at the end of 28 years, we need to calculate the compound value of beginning balance, withdrawals and deposits.

So, the Amount at the end of the period = Balance at the beginning * Compound value interest factor of $1 @5% for n years

As the withdrawals will be every other year beginning next year until 8 withdrawal so, the withdrawal will be till 16th Year and as the deposits will be every other year beginning two years from now until 8 deposits so, the deposits will be till 17th year

Taking into consideration of the above formula for the ending balance considering all deposits and withdrawals. the ending balance after 17 years will be $102,646.39 (see below table)

As there will be no further deposits or withdrawals so this balance after 17th year will be accumulated till 28th year that means the beginning balance of year 18 will be accumulated for 11 years (see below table)

So, the account balance after 28 years will be $259,387.42