Continuous Compound Interest Question (pre-calculus)

Question

(a) Suppose you deposit P dollars into a bank that pays an interest rate r compounded continuously. How long does it take to double your original deposit P.

 

(b) Suppose you deposit P dollars into a bank that compounds interest continuously. What is the interest rate r that doubles your original investment P after the first year.

 

The equation for continuous compound interest is A = Pe^rt where P = principal value, r = interest rate per year, t = time in years, A = amount, and e = the mathematical constant e 

 

I've been working on this question for hours now, but I don't know if the answers I got are correct so I would appreciate some confirmation

 

The answer I got for a. is t = (ln2A/P)/r

 

The answer I got for b. is r = (ln2A/P)/t

Answer 1

a) doubling time, compounding continuously: 2P = Pe^rt

2 =e^rt

ln 2 = rt

t = (ln 2)/r

 

b) find r so that account value doubles in one year!

 from the above, 1 = (ln 2)/r  so r = ln 2 = 0.693 which is 69.3% per year. Good luck finding a financial institution giving that kind of interest!