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)
........
click here to see the step by step calculation for t
........
t = 18.33 years
It will take 18.33 years.