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

MATH104 December 2013

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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.)

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

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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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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