numeric 1 point manny deposits $300 in a savings account that compounds annually at a rate of 3%. how much…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Solve for Manny's problem

For Manny: $P = 300$, $r=0.03$, $n = 1$ (compounded annually), and $t = 7$. Substitute into the formula: $A=300(1 + 0.03)^{7}$. First, calculate $(1 + 0.03)^{7}=1.03^{7}\approx1.22987386$. Then, $A = 300\times1.22987386\approx368.962158\approx369$.

Step3: Solve for Dwight's problem

For Dwight: $P = 4575$, $r = 0.00875$, $n = 4$ (compounded quarterly), and $t=\frac{3}{4}$ (since we want the third - quarter balance). Substitute into the formula: $A = 4575(1+\frac{0.00875}{4})^{4\times\frac{3}{4}}$. First, calculate $\frac{0.00875}{4}=0.0021875$. Then, $1+\frac{0.00875}{4}=1.0021875$. And $4\times\frac{3}{4}=3$. So, $A = 4575\times(1.0021875)^{3}$. $(1.0021875)^{3}=1.0021875\times1.0021875\times1.0021875\approx1.006562$. $A = 4575\times1.006562\approx4605$.

Answer:

1. 369
2. 4605