Final answer:
To calculate the rate compounded continuously, we can use the formula A = Pe^rt, where A is the future value, P is the present value, e is Euler's number, r is the interest rate, and t is the time in years. Substituting the given values into the formula, we find that the rate compounded continuously for this promissory note is approximately -8.55%.
Step-by-step explanation:
To calculate the rate compounded continuously, we can use the formula:
A = Pe rt
Where:
- A = the future value of the investment
- P = the present value of the investment
- e = Euler's number (approximately 2.71828)
- r = the interest rate
- t = the time in years
In this case, we have:
- A = $58,000
- P = $21,000
- t = 15 years
Substituting these values into the formula, we get:
$58,000 = $21,000e r * 15
Solving for r:
$21,000 / $58,000 = e 15r
e 15r = 0.3621
Taking the natural logarithm (ln) of both sides:
ln(0.3621) = 15r
r = ln(0.3621) / 15
Using a calculator, we find that r ≈ -0.0855
So, the rate compounded continuously that you would earn is approximately -0.0855, or -8.55%.