How long, to the nearest whole year will it take money to double if it is invested at 20% compounded annually?

Question

Compound interest problem 

Answer 1

the underlying formula that you want to use here to compute compound interest is

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

for this scenario that means taking

2P = P(1 + 0.20)^(1*t)

2 = (1.20)^t

t = log(2) / log(1.20) = 3.80

meaning that it will take approximately 3.80 years for the amount of money to double

Answer 2

M = amount of money as a function of time t in years.

 

M(t) = M(0) (1.20)^t

 

Solve for t from

 

2M(0) = M(0) (1.20)^t

 

2 = 1.20^t

 

log2 = t log1.20

 

t = log2 / log1.20 ≅ 3.802 years ≅ 4 years (to the nearest whole year)