The formula for determining continously compounded interest is expressed as
A = Pe^rt
where
A is the amount in the account after t years
P is the principal or amuount invested
r is the interest rate
From the information given,
A = 100000
P = 5000
r = 9.7% = 9.7/100 = 0.097
By substituting these values into the formula, we have
100000 = 5000 e^0.97t
Dividing both sides of the equation, we have
100000/5000 = e^0.097t
20 = e^0.097t
We would take the natuaral log of both sides of the equation. it becomes
ln 20 = lne^0.097t
By applying the law of logarithm on the right side of the equation,
ln 20 = 0.097tlne
Recall, ln e = 1
Thus, we have
ln 20 = 0.097t
t = ln20/0.097
t = 30.9
It will take 30.9 years
