Question

A building was bought for $110,000 and sold 20 years later for $420,000. What interest rate (compounded continuousiy) was eamed on the investment? To find the interest rate earned on this investment, use the formula for continuous compound interest, where A is the final amount, Pis the intial amount, t is the interest rate, and t is the fime period. What is the formula for continuous compound interest?

A. A=Pe −1
B. A=Pe n

Answer 1

To find the interest rate earned on an investment using continuous compound interest, we can use the formula A = Pe^(rt), where A is the final amount, P is the initial amount, r is the interest rate, and t is the time period in years. In this case, P is $110,000, A is $420,000, t is 20 years, and we need to solve for r. The interest rate earned on the investment, compounded continuously, is approximately 0.043 or 4.3%.

Step-by-step explanation:

To find the interest rate earned on an investment using continuous compound interest, we can use the formula A = Pe^(rt), where A is the final amount, P is the initial amount, r is the interest rate, and t is the time period in years. In this case, P is $110,000, A is $420,000, t is 20 years, and we need to solve for r. Let's plug in the values and solve for r:

$420,000 = $110,000 * e^(r * 20)

Divide both sides of the equation by $110,000:

4 = e^(20r)

Take the natural logarithm of both sides to isolate the exponent:

ln(4) = ln(e^(20r))

Using the property of logarithms, we can bring down the exponent:

ln(4) = 20r * ln(e)

Since ln(e) = 1, we can simplify the equation to:

ln(4) = 20r

Now, divide both sides by 20 to solve for r:

r = ln(4) / 20

Using a calculator to find the value of ln(4) and performing the division, we get:

r ≈ 0.043

Therefore, the interest rate earned on the investment, compounded continuously, is approximately 0.043 or 4.3%.