Question

You wish to accumulate $100,000 through monthly payments of $100. If you can earn interest at an annual rate of 4% compounded monthly, how long (to the nearest year) will it take to accomplish your goal? I just need the equation, can anyone help me?

Answer 1

u may use annuity formula

Answer 2

\(\large 100000 = 100\bullet \frac{(1+i)^{nt}-1}{i}\)

Answer 3

plugin the known values and solve \(t\)

Answer 4

first i have to divide 100000/1000 right?

Answer 5

sorry 100000/100

Answer 6

yes,
did u find \(i\) ?

Answer 7

yeah it is r/m or 0.04/12

Answer 8

yes!

keep going :)

Answer 9

I'm sorry, I love math, but sometimes I get confuse about formulas D:, then do i have to multiply 1,000 by .04/12?

Answer 10

correct !

Answer 11

you will have to use calculator...

Answer 12

yeah, but it is the same if first i multiply 1000 by 12 and then divide by .04? or I have to get first the answer of .04/12 ?

Answer 13

\(\large 100000 = 100\bullet \frac{(1+i)^{nt}-1}{i}\)

divide 100 both sides


\(\large \frac{100000}{100} = \frac{100\bullet \frac{(1+i)^{nt}-1}{i}}{100}\)

\(\large 1000 = \frac{(1+i)^{nt}-1}{i}\)

multiply \(i\) both sides :

\(\large 1000\times i = (1+i)^{nt}-1\)

add 1 both sides :

\(\large 1000\times i + 1 = (1+i)^{nt}\)

Answer 14

now plugin i = 0.04/12

Answer 15

\(\large 1000\times \frac{0.04}{12} + 1 = (1+\frac{0.04}{12})^{12t}\)

Answer 16

fine so far eh ?

Answer 17

Yeah!!! Thanks to be patient, sometimes I just get so confuse and I don't know if there's something wrong with my calculator D:

Answer 18

your calculation is perfectly fine :)

Answer 19

http://www.wolframalpha.com/input/?i=100000+%3D+100*%28%5Cfrac%7B%281%2B0.04%2F12%29%5E%7B12*t%7D-1%7D%7B0.04%2F12%7D%29

Answer 20

wolfram says \( t \approx 36.7\)
that means he has to wait \(\approx 37\) years

Answer 21

see if that looks okay...

Answer 22

Thank you!!!!!!!!!! You save my life!!

Answer 23

np :)

Answer 24

Well right now i know how to do the rest of my homework! Thank you so much! (: