Question

you make monthly deposits into an account earning 4.1% for 18 years. afterwards, you stop making deposits and withdraw $300 at the end of each month for 12 years. what must your monthly deposits be during the first 18 years? round to two decimal places.

Answer 1

Value of $300 withdrawn every year for 12 years (at t=18 years)

=

Present value of annuity

Present Value of annuity

=

P[{1-(1+r)^-n}/r]

where P

=

monthly withdrawl = $300

t

=

12 years*12 months =144

r

=

4.1%/12=0.3417% or 0.003417

PV of annuity

=

$300[{1-(1+0.003417)^-144}/0.003417]

=

$300[{1-0.6119}/0.003417]

=

$300[0.3811/0.003417]

=

$300*113.5833

=

$                             34,075.0

The future value of annuity of monthly payment at t=18yrs

=

Present value of annuity of $300 at t=18

Future value of annuity

=

P[{(1+r)^n}-1]/r

where P

=

Monthly payment

t

=

18yrs812 months=216

r

=

4.1%/12=0.3417% or 0.003417

therefore

$34,075

=

P[{(1+0.003417)^216}-1]/0.003417

$34,075

=

P[{(1.003417)^216}-1]/0.003417

$34,075

=

P{2.089268-1}/0.003417

$34,075

=

P*318.7791

$34075/318.7791

=

P

$106.89

=

P

Monthly payment to be deposited today =$106.89

There may be little difference due to decimal places.Please do not downvote on that basis

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