How much do I need to invest monthly to retire in 20 years and with 20,000 per year with a 7% rate compounded?

Question

I am in school at University of Phoenix and this was one of our discussion questions. The whole class is having trouble coming up with an answer. It's bugging the heck out of me. right now, my equation is

7/100 = 20,000/X

Which works out to 285,714.29 (after rounding to the nearest cent)

So that is the principle of what I need

From there, I need to figure out a payment schedual. I multiplied 12 * 20 (12 months in a year over 20 years) and came up with 240 months.

The answer to that after rounding is 1190.78

That didn't really seem right, so I figured that maybe I missed something with interest... anyone have an idea?

The 7% interest is compounded monthly

Answer 1

You are certainly getting a variety of answers.  The one I got working it out on my calculator but rounding off the monthly interest rate to 5 decimal places was $548.74 about.  

The equation is P*((1+i)**240-1)/i = 285,714.29 where P is the amount you are trying to find and i is 0.07/12 or 0.0058333333.....

Solving for P = 285,714.29/((1.00583**240)-1)/.00583..

= about $548.74

Taking the interest rate out to more decimal places will lower the amount that is needed to be invested a little.

Answer 2

PV = ??

FV=0 (assuming you are spending all your money)

PMT = 20,000/12=1,667

i=7/12=.5833333333

n=20*12=240 (assumes the average person lives 20 years in retirement)

PV=-215,013.83

So at retirement you would need approximately 215,014 lump sum.

Therefore,

FV=215,014

n=20

i=7

PV=55,563

So you would need to invest approx. 55,563  today to live off 20,000 annually in 20 years (not adjusted for inflation)

Alternately if you did not have the 55,563

PV=0

FV=215,014

n=20*12

i=7/12

PMT=-412.75

You could make a monthly investment of approx. 412.75 to reach your goal.

Answer 3

What you're missing is the interest earned on the savings per month.

7% annually is 0.5833% interest per month.

At $500 you'll earn $2.91 interest per month.

After the first month the person will have $1000 and they'll earn $5.83 per month.  And so on for the 240 months...

I'm not a mathematician so I don't know the formula, but in excel it's =PMT( 0.005833,240 , , -285714.29 ,1)

If you save $545.29 every month, you'll be able to live off $20k per year at 7% in 10yrs.  The magic of compound interest.

I pity those fools who spend $500 per month on their credit card.

Answer 4

i found a video that can answer this http://www.youtube.com/watch?v=UmktUbRGG...