Problema Solution

How long will it take for ​$

6 comma 200

6,200 to grow to ​$

36 comma 700

36,700 at an interest rate of

9.7

9.7​% if the interest is compounded​ continuously? Round the number of years to the nearest hundredth.

Answer provided by our tutors

Let

P = $6,200 the principal
A = $36,700 the future value
t = the time needed

Compounded​ continuously at rate of r = 0.097 or 9.7%:

A=Pe^(rt)
A=6200e^(0.097*t)
6200e^(0.097*t) = 36700

e^(0.097*t) = 36700/6200

0.097t = ln(36700/6200)

t = (1/0.097) ln(36700/6200)

........

click here to see the step by step calculation for t

........

t = 18.33 years

It will take 18.33 years.