question 26 (3 points)\nyou decided to move from cumberland county, tn to sumner county, tn. based on the…

question 26 (3 points)\nyou decided to move from cumberland county, tn to sumner county, tn. based on the percent - change for food costs from the cost of living calculator, how much can you expect to pay for food in sumner county if you paid an average of $314.40 for food in cumberland county?\nenter the dollar amount rounded to the nearest cent.\nyour answer:\nanswer\nquestion 27 (3 points)\nhow much money should be deposited today in an account that earns 4.66% compounded daily so that it will accumulate to $44,850 in 12 years?\nuse this formula:\n$pv=\frac{fv}{(1 + \frac{r}{n})^{nt}}$\nenter the dollar amount rounded up to the nearest cent.\nyour answer:\nanswer

question 26 (3 points)\nyou decided to move from cumberland county, tn to sumner county, tn. based on the percent - change for food costs from the cost of living calculator, how much can you expect to pay for food in sumner county if you paid an average of $314.40 for food in cumberland county?\nenter the dollar amount rounded to the nearest cent.\nyour answer:\nanswer\nquestion 27 (3 points)\nhow much money should be deposited today in an account that earns 4.66% compounded daily so that it will accumulate to $44,850 in 12 years?\nuse this formula:\n$pv=\frac{fv}{(1 + \frac{r}{n})^{nt}}$\nenter the dollar amount rounded up to the nearest cent.\nyour answer:\nanswer

Answer

Explanation:

Step1: Identify the formula for compound - interest

The present - value formula for compound interest is $PV=\frac{FV}{(1 + \frac{r}{n})^{nt}}$, where $PV$ is the present value (the amount to be deposited today), $FV$ is the future value ($FV = 44850$), $r$ is the annual interest rate ($r=0.0466$), $n$ is the number of times compounded per year ($n = 365$ for daily compounding), and $t$ is the number of years ($t = 12$).

Step2: Substitute the values into the formula

First, calculate the exponent $(1+\frac{r}{n})^{nt}$. $\frac{r}{n}=\frac{0.0466}{365}\approx0.000127671$ $nt=365\times12 = 4380$ $(1+\frac{r}{n})^{nt}=(1 + 0.000127671)^{4380}$ Using a calculator, $(1 + 0.000127671)^{4380}\approx1.74477$ Then, $PV=\frac{FV}{(1+\frac{r}{n})^{nt}}=\frac{44850}{1.74477}\approx25704.33$

Answer:

$25704.33$