how many years will it take for $500 to grow to $1,051.82 at 9% interest compounded annually

Question

need to know the equation to use

 

Answer 1

Compound interest:

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

A = future amount = 1051.82

p = principal investment = 500

r = interest rate = .09

n = # times compounded per year = 1

t = time in years

 

1051.82 = 500(1.09)^t

 

1051.82/500 = 1.09^t

 

log(1051.82/500) = log(1.09^t)

log(1051.82/500) = t[log(1.09)]

 

t = [log(1051.82/500)/log(1.09)]

 

t = 8.63 years