Question

You would like to retire in 16 years. Starting in 16 years you will receive your first of 198 monthly payments of $2,000. You will pay for your retirement by making monthly deposits for 16 years starting today. Find the size of these deposits if your funds will earn J12 =12%

Answer 1

Starting in 16 years Annuity Received (P)= 198

Number of month (n)= 198

J12=12%

Monthly rate (I)= 12%/12= 1%

Payment start in 16 years. So it starts at Beginning, it is an annuity due.

Present value of Annuity due formula = P+(P*(1-(1/(1+I)^(n-1)))/I)

=2000 +(2000*(1-(1/(1+1%)^(198-1)))/1%)

=173834.3771

Amount to be accumulated in 16 years is present value of Annuity wirhdrawal that is now future value =173834.3771

Number of month in 16 years (n)= 16*12=192

Interest rate per month (I)= 12%/12= 1%

Payment start to be made at today. So it is Annuity due.

Future value of Annuity due formula = P+(P*(((1+I)^n)-1)/i

173834.3771 = P+(P*(((1+1%)^192)-1)/1%)

173834.3771= P+ 575.6219742P

173834.3771/576.6219742= P

P=301.4702611

So Amount Required to save each month is $301.47