Question 1143333: A promissory note will pay $59,000 at maturity 21 years from now. If you pay $20,000 for the note now, what rate compounded continuously would you earn?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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