Question

A savings account earns 4.62% annual interest, compounded continuously. After approximately how many years will a principal of $500 double?

Answer 1

2p=pe^rt
2=e^rt
2=e^0.0462t
0.0462t=log(2)/log(e)
t=0.6931471805/0.0462
t=15 years

Answer 2

Solve for "years" (t)

A=P e^(rt)

A=1000
P=500
e=e
r=0.0462

Solve for t: use natural logarithms

(0.0462)t=in 2

t=15 years