Question

What annual rate with continuous compounding would be required for a debt of $1,991 to grow into $3,424 in 16.5 years? In this question you will need to solve for r in FV = PVert. Start by dividing both sides by PV. Then use logarithms to "bring down" the exponent. Round your answer to the nearest tenth of a percent.

Answer 1

To find the annual rate with continuous compounding, use the formula FV = PV * e^(r*t), where FV is the future value, PV is the present value, r is the annual interest rate, and t is the time in years. Plugging in the values from the question and solving for r, we find that the annual rate required for the debt to grow into $3,424 in 16.5 years is approximately 4.08%.

Step-by-step explanation:

To solve for the annual rate with continuous compounding, we can use the formula for compound interest:

FV = PV * e^(r*t)

Where FV is the future value, PV is the present value, r is the annual interest rate, and t is the time in years.

Plugging in the values from the question, we have:

3424 = 1991 * e^(r*16.5)

Dividing both sides by 1991 and taking the natural logarithm of both sides, we get:

ln(3424/1991) = r * 16.5

Solving for r, we have:

r = ln(3424/1991) / 16.5

Using a calculator, we find that r is approximately 0.0408 or 4.08% (rounded to the nearest tenth of a percent).