Can you find the answer to problem 37 if the interest is compounded daily?

Question

This is from Chapter 9, Exercise 9-4, #38 of Fundamentals of Technical Mathematics (2nd edition): Interest on savings accounts is compounded daily in most banks. An approximate formula for the amount A after n year(s) compounded daily is A = Pe^rn, where P = principal and r = interest rate per year. Find the answer to problem 37 if the interest is compounded daily. (This formula is for continuous compounding, that is, compounding every instant, which is very close to daily compounding. In Virginia, banks compound continuously.)

Problem #37:

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Answer 1

How many years will it take for money to double when it is compounded yearly at 6 percent per year?

Let x be the number of years.

Daily compounding:
(1 + 0.06 / 365.25)^(365.25x) = 2
365.25x log (1 + 0.06 / 365.25) = log(2)
x = log(2) / 365.25 log(1 + 0.06 / 365.25)
= 11.553yr.

Continuous compounding:
e^(0.06x) = 2
0.06x = ln(2)
x = ln(2) / 0.06
= 11.552yr.