Derek wants to withdraw $13,242.00 from his account 4.00 years from today and $13,962.00 from his...

Derek wants to withdraw $13,242.00 from his account 4.00 years from today and $13,962.00 from his account 14.00 years from today. He currently has $3,676.00 in the account. How much must he deposit each year for the next 14.0 years? Assume a 5.93% interest rate. His account must equal zero by year 14.0 but may be negative prior to that. round answer 2 decimal places

Expert Solution

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

Future value of withdrawals=13,242*(1.0593)^10+13,962

=37520.2652

Future value of current balance=3,676*(1.0593)^14

=$8234.57358

Future value of annual deposits=Annuity[(1+rate)^time period-1]/rate

=Annuity[(1.0593)^14-1]/0.0593

=Annuity*20.9121542

Hence for balance to be zero;

Future value of withdrawals=Future value of deposits

37520.2652=8234.57358+Annuity*20.9121542

Annuity=(37520.2652-8234.57358)/20.9121542

=$1400.41(Approx)

jeff jeffy answered 2 years ago

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