Question

You invest $2500 in an account at interest rate r, compounded continuously. Find the time required for the amount to double and triple. (Round your answers to twodecimal places.)r = 0.0465(a) doubleyr(b) tripleуг

Answer 1

P= 2500

r= 0.0465

A= P. e^(rt)

Where:

A = final mount

P = principal investment

r= rate

T= time (years)

To double it:

2 x 2500 = 2500 e^(0.0465 x t)

(2 x2500)/2500= e^(0.0465 x t)

2= e^(0.0465 x t)

Ln 2 = Ln e^(0.0465 x t)

Ln2 =0.0465t (Ln e)

Ln2 = 0.0465 t

t = Ln2 /0.0465

t= 14.91 years

Triple:

3 x2500 = 2500 e^(0.0465 t)

(3 x 2500 ) /2500 = e^(0.0465 t)

3 = e^(0.0465 t)

ln3 = ln e^(0.0465 t)

ln3 = 0.0465t Lne

ln3= 0.0465t

ln3/0.0465 =t

t= 23.63 y