Science:Math Exam Resources/Courses/MATH104/December 2013/Question 01 (h)

MATH104 December 2013

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[hide] Question 01 (h)
You borrow 10 thousand dollars from Nick the Shark, who charges you at a fixed rate r that is compounded continuously. If you pay Nick 100 thousand dollars 2 years later, what was the annual rate of interest that he charged? (A calculator-ready form will suffice.)

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[show] Hint
Recall that the formula for continuously compounded interest is given by $\displaystyle A=Pe^{rt}$, where A is the new amount, P is the principal, r is the interest rate, and t is the time.

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[show] Solution
For continuously compounded interest, we have the formula $\displaystyle A=Pe^{rt}$ where A is the amount, P is the principal, r is the rate, and t is the time. We are given that $\displaystyle P=10000,A=100000,t=2$. Plugging these in yields ${\begin{aligned}100000&=10000e^{2r}\\10&=e^{2r}\\\ln 10&=2r\\r&={\color {blue}{\frac {\ln 10}{2}}}\end{aligned}}$

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