Question

Suppose that $12,000 is invested in a bond fund, and the account grows to $13,832.03 in 5 years. Use the model A=Pe^rt to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. Avoid rounding in intermediate steps.

a) 3.2%
b) 4.8%
c) 6.2%
d) 7.1%

Answer 1

To determine the average rate of return under continuous compounding, we use the formula A = Pe^rt. In this case, the average rate of return is approximately 3.0%.

Step-by-step explanation:

To determine the average rate of return under continuous compounding, we can use the formula A = Pe^rt, where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years.

In this case, we have P = $12,000, A = $13,832.03, and t = 5 years. Plugging these values into the formula, we get:

13,832.03 = 12000 * e^(5r)

Dividing both sides by 12000, we have:

e^(5r) = 13,832.03 / 12000

Taking the natural logarithm of both sides, we get:

ln(e^(5r)) = ln(13,832.03 / 12000)

Using the property of logarithms, ln(e^(5r)) simplifies to 5r:

5r = ln(13,832.03 / 12000)

Dividing both sides by 5, we have:

r = ln(13,832.03 / 12000) / 5

Using a calculator, we can calculate the value of r to be approximately 0.0302.

Finally, we convert this decimal value to a percentage by multiplying by 100:

The average rate of return under continuous compounding is approximately 3.0%.