Word Problem

Question

I have a problem picking out a problem from word questions. Can someone please help me.

 

Suppose $1,500 is invested in an account at an annual interest rate of 4.2% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size?

Answer 1

A = pe^rt, where A = final amount, p = principal, e = Euler's number, t = time, r = rate

 

3000 = 1500e^0.042t         divide both sides by 1500

2 = e^0.042t                       take ln of both sides

ln 2 = ln e^0.042t               calculate

0.693147181 ≈ 0.042t   divide both sides by 0.042

16.5035 ≈ t

 

The amount doubles in about 16.5 years.