question hakeem invested $3,500 in an account paying an interest rate of 8 7/8% compounded daily. salma…

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the number of years. For Hakeem, $P=$3500$, $r = 0.0825$, and $t = 6$. So, $A_{Hakeem}=3500\times e^{0.0825\times6}$. $A_{Hakeem}=3500\times e^{0.495}$ Using a calculator, $e^{0.495}\approx1.640237$, so $A_{Hakeem}=3500\times1.640237\approx5740.83$.

Step2: Recall daily - compounding formula

The formula for compound interest compounded $n$ times a year is $A=P(1 +\frac{r}{n})^{nt}$. When compounded daily, $n = 365$. For Salma, $P = 3500$, $r=0.0875$, and $t = 6$. So, $A_{Salma}=3500\times(1+\frac{0.0875}{365})^{365\times6}$. First, calculate $\frac{0.0875}{365}\approx0.000239726$. Then $1+\frac{0.0875}{365}\approx1.000239726$. $365\times6 = 2190$. So, $A_{Salma}=3500\times(1.000239726)^{2190}$. Using a calculator, $(1.000239726)^{2190}\approx1.690977$. So, $A_{Salma}=3500\times1.690977\approx5918.42$.

Step3: Find the difference

The difference $\Delta A=A_{Salma}-A_{Hakeem}=5918.42 - 5740.83=177.59\approx178$.

Answer:

178