Final answer:
The continuous compounding rate earned on an investment of $28,000 to reach $44,000 in 7 years is approximately 6.000%, after calculating the natural logarithm of the ratio of the matured amount to the principal and dividing by the time period.
Step-by-step explanation:
To calculate the rate compounded continuously that would earn an investor $44,000 at maturity 7 years from now, after paying $28,000 for the promissory note now, you can use the formula for continuous compounding which is:
A = Pert
Here, A represents the amount of money accumulated after n years, including interest, P is the principal amount (the initial sum of money), r is the annual interest rate (in decimal), t is the time the money is invested for in years, and e is the base of the natural logarithm approximately equal to 2.71828.
We know that A = $44,000, P = $28,000, and t = 7 years. We need to find the rate r. The equation to solve is:
44000 = 28000e7r
Solving for r, we get:
r = ln(44000/28000) / 7
By calculating this, we find that the investment would earn approximately:
r ≈ 0.060 or 6.000% compounded continuously.