Question 1143333
continuous compounding formula is f = p * e ^ (r * t)


f = future value = 59,000
p = present value = 20,000
n = 21


you want to solve for r.


formula becomes 59,000 = 20,000 * e ^ (r * 21)


divide both sides of he formula by 20,000 to get 2.95 = e ^ (r * 21)


take the natural log of both sides of the equation to get ln(2.95) = ln(e ^ (r * 21))


since ln(e ^ (r * 21) = r * 21 * ln(e) and since ln(e) = 1, the formula becomes:


ln(2.95) = r * 21


solve for r to get r = ln(2.95) / 21 = 0.051514532


confirm by replacing r in the original equation to get:


59,000 = 20,000 * e ^ 0.051514532 * 21)


this results in 50,000 = 50,000, confirming the solution is correct.