Question

You estimate you’ll need $9,000 per month for 30 years starting one month from your 65^th birthday to live on during your retirement. Today is your 40^th birthday and you want to make equal monthly deposits into an account paying 4% per year, the first deposit in one month. How much must each deposit be, so you can pay yourself $9,000/Mo for 30 yrs. starting in 25 yrs.?

***Please use financial calculator with steps written down for the keystrokes***

Answer 1

First we calculate the Present value of payments to be received after 65th birthday

Using a financial calculator

FV= 0 (Press 0 followed by FV)

PMT = 9000 (Press 9000 followed by PMT)

N = 360 (30years*12 payments per year = 360 periods) (Press 360 followed by N)

I/Y = 4/12 (4%/12 = 0.3333% rate per quarterly period) (Press 0.3333 followed by I/Y)

cpt PV, we get PV = 1885151.16

Hence, after 25 years $1885151.16 to be accumulated in the account for the goal to be achieved

Now, we calculate the amount of each deposit

Using a financial calculator

FV= -1885151.16 (Press 1885151.16 followed by +/- and then press FV)

PV = 0 (Press 0 followed by PV)

N = 300 (25years*12 payments per year = 300 periods) (Press 300 followed by N)

I/Y = 4/12 (4%/12 = 0.3333% rate per quarterly period) (Press 0.3333 followed by I/Y)

cpt PMT, we get PMT= 3666.69

Hence, each deposit should be of $3666.69