a promissory note will pay $44,000 at maturity 5 years from now. If you pay $28,000 for the note now, what rate compounded continuously would you earn?
To find the rate compounded continuously, we can use the formula for compound interest:
A = P * e^(rt)
Where:
A = Final amount (maturity value) = $44,000
P = Initial investment (present value) = $28,000
r = Interest rate
t = Time period = 5 years
e = Euler's number, approximately 2.71828
We can rearrange the formula to solve for the interest rate (r):
r = ln(A/P) / t
Where ln denotes the natural logarithm.
Let's plug in the given values and calculate the rate:
r = ln(44000/28000) / 5
To calculate this using a calculator or a tool like Python, we can use the logarithm function with the base e (natural logarithm):
r ≈ ln(1.5714) / 5
Now, we can calculate the natural logarithm of 1.5714:
ln(1.5714) ≈ 0.4519
Substituting this back into the equation:
r ≈ 0.4519 / 5
Finally, we can calculate the interest rate:
r ≈ 0.0904 or 9.04%
Therefore, the rate compounded continuously that you would earn on the promissory note is approximately 9.04%.