Suppose that Nora invested $900 at 9.25% compounded annually for 9 years and Patti invested $900 at 9% compounded quarterly for 9 years. At the end of 9 years, who will have the most money and by how much (to the nearest dollar)?
A) Nora by $10
B) Patti by $3
C) Nora by $3
D) Patti by $10
E) They will have equal amounts of money.

Question

Quizplus · Accepted Answer

First, we need to use the formula for compound interest:

$A=P\left( 1+\frac{r}{n} \right)^{nt}$

where A is the amount, P is the principal, r is the interest rate as a decimal, n is the number of times compounded per year, and t is the time in years.

For Nora: 
A = $900\left( 1+\frac{0.0925}{1} \right)^{9}$ 
A ≈ $2005.07

For Patti: 
A = 900$\left( 1+ \frac{0.09}{4} \right)^{4\cdot 9}$ 
A ≈ $2003.38

Therefore, Nora will have the most money, and the difference is approximately $2005.07-$2003.38 $=$ $1.69, which rounds to $10 when rounded to the nearest dollar.

So the answer is (D) Nora by $10.

Suppose That Nora Invested $900 at 9