If $5000 is invested at an interest rate k, compounded continuousy and grow to $6953.84 in 6 years what is the

Question

If $5000 is invested at an interest rate k, compounded continuously and grow to $6953.84 in 6 years is the interest rate
k=0.055
k = 5.5%

or

k = 0.056515 = 5.65%

Answer 1

For k compounding continuously the formula is

the exponential e^(nk)
where k is the annual interest rate and n is the number of years.

In 6 years,
5000*e^(6k) = 6953.84
e^(6k) = 6953.84/5000 = 1.390768

take the natural logarithm of both sides
6k = 0.329856

k = 0.054976 or 5.5%
.

Answer 2

S = P * e^(rt)
6953.84 = 5000 * e^(6r)
1.390768 = e^(6r)
LN1.390768 = LN e^(6r) = 6r
.329856 = 6r
r = .054976
or 5.5% rounded