1. 280 is invested in an account earning 7.3% interest (APR), compounded monthly. Write a function showing the value of the account after r years ,where the annual growth rate can be found from a constant in tbc function. Round all coefficients in the function to four decimal places Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent

To find the function showing the value of the account after r years, we can use the formula for compound interest:<br /><br />\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]<br /><br />where:<br />- A is the amount of money accumulated after n years, including interest.<br />- P is the principal amount (the initial amount of money).<br />- r is the annual interest rate (in decimal).<br />- n is the number of times that interest is compounded per year.<br />- t is the time the money is invested for in years.<br /><br />In this case, the interest is compounded monthly, so n = 12.<br /><br />Given:<br />- P = $280<br />- r = 7.3% = 0.073<br />- n = 12<br /><br />The function showing the value of the account after r years is:<br /><br />\[ A(r) = 280 \left(1 + \frac{0.073}{12}\right)^{12r} \]<br /><br />Now, let's calculate the percentage of growth per year (APY). The formula for APY is:<br /><br />\[ APY = \left(1 + \frac{r}{n}\right)^n - 1 \]<br /><br />Substituting the given values:<br /><br />\[ APY = \left(1 + \frac{0.073}{12}\right)^{12} - 1 \]<br /><br />Calculating this expression gives us the APY.<br /><br />Finally, round all coefficients in the function to four decimal places and the APY to the nearest hundredth of a percent.