what interest rate is required for an investment subject to continuous compounding to triple in 15 years?

A= Pe^rt ?

e^15r = 3

15r = ln3
r = ln3/15 = 7.3%

I have the same question except mine is 5 years. Using this formula, I don't even come close to the correct answer in the book. Please advise.

To determine the interest rate required for an investment subject to continuous compounding to triple in 15 years, we can use the formula you provided: A = Pe^rt.

In this formula:
- A represents the future value of the investment.
- P represents the present value (initial investment).
- e is a mathematical constant approximately equal to 2.71828.
- r represents the interest rate.
- t represents the time (in years) the investment is held.

In this case, we want the investment to triple, which means the future value (A) will be three times the present value (P).

Let's rewrite the formula to represent this scenario:
3P = Pe^rt

Now, we can cancel out the common factor of P:
3 = e^rt

To solve for the interest rate (r), we need to isolate it. Take the natural logarithm (ln) of both sides of the equation:
ln(3) = ln(e^rt)

By applying the logarithm property, we bring the exponent down:
ln(3) = rt * ln(e)

Since ln(e) is equal to 1, the equation simplifies to:
ln(3) = rt

Now, we can solve for the interest rate (r) by dividing both sides of the equation by t:
r = ln(3) / t

Plugging in the values, we can calculate the interest rate required for the investment to triple in 15 years:
r = ln(3) / 15 ≈ 0.0739 or 7.39%

Therefore, an interest rate of approximately 7.39% per year would be required for an investment subject to continuous compounding to triple in 15 years.