Question

if $5000 grows to $5623.12 after 1 year, with interest compouded continuously, what is the interest rate. how long will it take the original amount to grow?

Answer 1

If $5000 grows to $5623.12 after 1 year, with interest compouded continuously,
then to find interest rate we use the formula:
A = P*e^(r*t),
where A is final amount, P is principal, r is interest rate, t is time.
5623.12 = 5000*e^(r*1),
e^r = 1.125,
r = ln(1.125) = 0.1178 or 11.78%.
Then A = P*e^(0.1178t), hence t=1/0.1178*ln(A/P)=8.489ln(A/P).