Question

to review what youve learned. it will not count toward your grade. the amount of money, a, earned after being compounded monthly for t years with winton savings bank is represented by the function $f(t) = 500(1.005)^{12t}$. select the correct answers from the lists. (2 points) the initial amount of money invested is $\square$. the amount of money in the account $\square$ by about $\square$% each year.

Explanation:

Step1: Find Initial Amount

The compound interest formula is $A = P(1 + \frac{r}{n})^{nt}$, where $P$ is principal (initial amount). Given $f(t)=500(1.005)^{12t}$, when $t = 0$, $f(0)=500(1.005)^{0}=500$. So initial amount is $500$.

Step2: Analyze Growth Factor

Rewrite $f(t)=500(1.005)^{12t}=500((1.005)^{12})^{t}$. Calculate $(1.005)^{12}\approx1.061678$. So the annual growth factor is about $1.0617$, meaning growth (since factor > 1) by about $6.17\%$ (or approximately $6\%$ when rounded, but more accurately, $(1.005)^{12}-1\approx0.0617$ or $6.17\%$).

Answer:

The initial amount of money invested is $\boldsymbol{500}$. The amount of money in the account $\boldsymbol{\text{increases}}$ by about $\boldsymbol{6.17}$ (or $\boldsymbol{6}$ if approximate) $\%$ each year. (For the dropdowns, first is 500, second is "increases", third is ~6.17 or 6 depending on options.)