If the interest on a long-term Canadian(3/8%) investment is compounded continuously, how long will it take the value of an investment to triple? (Give the answer correct to two decimal places.)

Question

If the interest on a long-term Canadian(3/8%) investment is compounded continuously, how long will it take the value of an investment to triple? (Give the answer correct to two decimal places.)

Got 19 years--its wrong, can't find reason.

Thanks.

Answer 1

With continuous compounding,

A = A0*e^(r*t) = 3 A0
where A0 is the inityial principle,
r is the annual interest rate (0.375%)
t is the period of investment, in years.
e^(rt) = 3
rt = ln3 = 1.099
t = 1.099/0.00375 = 293 years

That's a pretty bad investment. Worse that US long term treasuries at current rates.

Answer 2

To determine the amount of time it takes for an investment to triple, when the interest is compounded continuously, we can use the continuous compound interest formula:

A = P * e^(rt)

Where:
A is the final amount (triple the initial investment)
P is the initial principal amount (the initial investment)
e is Euler's number (approximately equal to 2.71828)
r is the interest rate (in decimal form)
t is the time (in years)

In this case, we want to triple the initial investment, so A = 3P. The interest rate is given as 3/8%, which is equivalent to 0.0375 as a decimal. We need to solve for t, the time it takes for the value of the investment to triple.

Let's substitute the given values into the formula:

3P = P * e^(0.0375t)

Now, divide both sides of the equation by P:

3 = e^(0.0375t)

To isolate t, we need to take the natural logarithm (ln) of both sides of the equation:

ln(3) = ln(e^(0.0375t))

Since ln(e^x) = x, we can rewrite the equation as:

ln(3) = 0.0375t

Now, solve for t by dividing both sides of the equation by 0.0375:

t = ln(3) / 0.0375

Using a calculator, the approximate value of ln(3) is 1.0986. Dividing this by 0.0375 gives us:

t ≈ 29.29 years (rounded to two decimal places)

Therefore, it will take approximately 29.29 years for the value of the investment to triple when the interest is compounded continuously.

If you received a different answer of 19 years, it is likely that a calculation error occurred. Please double-check your calculations using the steps outlined above.