You want to have $100,000 when you retire in 30 years. If you can earn 4% interest compounded monthly, how much would you need to deposit now into the account to reach your retirement goal?

Question

anonymous · Answer

ok, I can help you

anonymous · Answer

awesome!

anonymous · Answer

first, set up the equation

anonymous · Answer

100000=a(0.04)^30

anonymous · Answer

y=ab^x

anonymous · Answer

scratch that, sorry I'm tired

anonymous · Answer

its alright haha

anonymous · Answer

yeah you are right, 10,000=ab^x

anonymous · Answer

ok we want a growth of 0.04 or 4%

anonymous · Answer

whats next

anonymous · Answer

1.04

anonymous · Answer

This will substitute b

anonymous · Answer

100000=a(1.04)^30

anonymous · Answer

NICE. You read my mind

anonymous · Answer

Now what

jim_thompson5910 · Answer

that equation would work if you are compounding annually

anonymous · Answer

now just work backwards (I think (I don't know it might be the sleep))

anonymous · Answer

we dont have a yet so we dont do that yet

anonymous · Answer

how do I find A??

anonymous · Answer

actually @jim_thompson5910  is right

anonymous · Answer

it's a monthly payment, and you are using the year

anonymous · Answer

so we need to find how many months are in 30 years

anonymous · Answer

100000=a(1.48)^360

anonymous · Answer

there now how do i find a

anonymous · Answer

nice now we need to divide 10,000 by 1.04^360 to find a

jim_thompson5910 · Answer

4% annual rate

4/12 = 0.333% monthly rate

so instead of 1.04 it should be 1.003333

anonymous · Answer

... wow, I'm very tired. I can't believe I missed that. He's right *Slaps self*

anonymous · Answer

ok now what

anonymous · Answer

wait @jim_thompson5910  wouldn't it be 33.3% not 0.333%

anonymous · Answer

which i dont think you're right jim, you are suppose to do .04/12

anonymous · Answer

then It would be 3.33%

jim_thompson5910 · Answer

(4%)/12 = 0.33333%

the 4% will get smaller and it won't increase to 33.33%

jim_thompson5910 · Answer

or yeah you could do 0.04/12 = 0.00333...

anonymous · Answer

ok nvm. So you have 10,000 / 1.00333^360 = A

anonymous · Answer

100000=a(1.003333)^360

anonymous · Answer

how do i find a

jim_thompson5910 · Answer

divide both sides by (1.003333)^360

anonymous · Answer

100000/3.3131?

anonymous · Answer

that's what I said, "10,000 / 1.00333^360"

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

yeah you just compute 100000/3.3131 now

anonymous · Answer

I got 30183.2121 but thats wrong

jim_thompson5910 · Answer

did you round to the nearest penny?

anonymous · Answer

yes

anonymous · Answer

its actually 30179.59, you did something wrong i dunno

jim_thompson5910 · Answer

ok try typing in (1+0.04/12)^(360) as the denominator
to ensure there is no rounding error

jim_thompson5910 · Answer

use a calculator like this one http://web2.0calc.com/ if you don't have a calculator like a TI83

jim_thompson5910 · Answer

http://web2.0calc.com/#100000/(1+0.04/12)^(360)

jim_thompson5910 · Answer

when you click the link, hit the "=" button on the calculator to have it compute the answer

anonymous · Answer

Hey guys I'm back, I had to go to the bathroom, and then help my dad, sorry.

anonymous · Answer

I'm constantly getting 3021.57 on the Bing calculator. I'm going to double check

anonymous · Answer

When I insert it into the equation, I get 9999.99889

anonymous · Answer

I think it would be safe to round it, so my answer would be 3021.57 for your question.