Interest compounded annually

Question

You place $800 in an account that earns 4% annual interest, compounded annually. How long will it be until you have $2000?

Answer 1

Define terms:

A = amount  = $2000

P = principle (amount put down in the beginning) = $800

r = interest rate (per year) = 4% = 0.04

t = number of years (what we are solving for)

 

Equation to calculate:

 

A = P (1 + r/n)^nt

 

n is the number of time the interest is compounded per year (in this case, n=1 since the interest is compounded annually)

 

So we have a simplified equation:

 

A = P (1 + r)^t

 

Plug in numbers:

 

2000 = 800(1.04)^t

2.5 = 1.04^t

 

Take natural log of both sides

 

ln 2.5 = t * ln 1.04

 

0.916 = t * 0.0392

 

t = 23.367 = 24 years (we round up since it will take more than 23 years to reach 2000)