Suppose that Nora invested $400 at 8.5% compounded annually for 6 years and Patti invested $400 at 8% compounded quarterly for 6 years. At the end of 6 years, who will have the most money and by how much (to the nearest dollar)?
A)Patti by $9
B)Nora by $1
C)Patti by $1
D)Nora by $9
E)They will have equal amounts of money.

Question

Quizplus · Accepted Answer

To determine who will have the most money and by how much, we calculate the future value for both Nora and Patti's investments using the formula for compound interest: $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.For Nora, the investment is compounded annually ($n = 1$), so the calculation is straightforward:- $P = $400$- $r = 8.5\% = 0.085$- $n = 1$- $t = 6$$$A_{Nora} = 400(1 + \frac{0.085}{1})^{1 \times 6} = 400(1.085)^6 \approx \$610.79$$For Patti, the investment is compounded quarterly ($n = 4$), so:- $P = $400$- $r = 8\% = 0.08$- $n = 4$- $t = 6$$$A_{Patti} = 400(1 + \frac{0.08}{4})^{4 \times 6} = 400(1 + 0.02)^{24} = 400(1.02)^{24} \approx \$601.80$$Comparing the two amounts, Nora has more money than Patti by approximately $610.79 - 601.80 = \$8.99$, which rounds to \$9.Therefore, Nora will have more money than Patti by about $9.

Suppose That Nora Invested $400 at 8