How long will it take for $2500.00 to grow to $100,000.00 if it grows with rate of 9% compounded monthly? Round the answer to three digits after the decimal.

Question

Not sure how to do this, if you can show me step by step that would be awesome!

Answer 1

The equation for compounding interest is:

T=P*(1+r/n)^n*t

where:
T=total amount
P=principal
r=annual interest rate
n=frequency of compounding per year
t=number of years

 

In this case:

T=100,000

P=2500

r=0.09

n=12

 

So solving for t

100000=2500*(1+0.09/12)^(12*t)

100000=2500*(1.0075)^(12t)

40=1.0075^(12t)

12t=log(base 1.0075)[40]=log(base10)[40]/log(base10)[1.0075)

12t=493.693

t=41.141 years