Question

A building was bought for $110,000 and sold 15 years later for $490,000. What interest rate (compounded continuously) was earned on the investment? Substitute the given values of A, P, and t into the formula. What is the next logical step to solve this equation for r? A. Divide both sides of the equation by 490,000 . B. Divide both sides of the equation by e r(15)

Answer 1

To solve for the interest rate (r) in a continuously compounded interest formula, substitute the given values into the formula P*e^(rt) = A and isolate r by dividing both sides of the equation by the initial investment. Then, take the natural logarithm of both sides of the equation and solve for r.

Step-by-step explanation:

To solve for the interest rate (r) in a continuously compounded interest formula, we can use the formula P*e^(rt) = A, where P is the initial investment, e is Euler's number (approximately equal to 2.71828), r is the interest rate, t is the time period in years, and A is the final value of the investment.

Substituting the given values into the formula, we have:

110,000 * e^(r*15) = 490,000

To isolate r, we need to divide both sides of the equation by 110,000, giving us:

e^(r*15) = 490,000 / 110,000

To simplify further, we can take the natural logarithm of both sides of the equation:

ln(e^(r*15)) = ln(490,000 / 110,000)

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

r*15 * ln(e) = ln(490,000 / 110,000)

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

r*15 = ln(490,000 / 110,000)

Finally, we divide both sides of the equation by 15 to solve for r:

r = ln(490,000 / 110,000) / 15