Hey everyone,
Today’s problem uses four new commands: left(, right), approx, and %, which represent the left and right delimiters (parentheses), the approximation symbol, and the percent sign, respectively.
Problem 2:
Mr. Burns deposits $3000 in a five-year certificate of deposit. At maturity the balance is $4,264.28. Find the annual effective rate of interest governing the account.
Solution 2:
Let i be the annual effective rate of interest. We want to use the relationship:
$latex displaystyle 3000(1+i)^5=4264.28$
to solve for i. The term (1+i)5 means that the $3000 in the account grew at an annual effective rate of interest i for five years.
$latex displaystyle (1+i)^5=frac{4264.28}{3000}$
Divide both sides by 3000.
$latex displaystyle 1+i=left(frac{4264.28}{3000}right)^frac{1}{5}$
Raise both sides to the 1/5 power.
$latex displaystyle i=left(frac{4264.28}{3000}right)^frac{1}{5}-1approx 7.2864541%$
Subtract 1 from both sides to yield the result. A very high yield for a CD!
Note: I’ve noticed that the $latex LaTeX$ support in WordPress doesn’t like currency symbols so I won’t be able to use them in my equations. So, any further financial problems I write will have to do without them (unless I figure out how to incorporate the symbols).