find the future value, using the future value formula and a calculator. (round your answer to the nearest…

Explanation:

Step1: Identify the 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 compounded per year, and (t) is the number of years. Given (P=$247500), (r = 8.09%=0.0809), (n = 365) (compounded daily), and (t = 30) years.

Step2: Substitute the values into the formula

Substitute (P = 247500), (r=0.0809), (n = 365), and (t = 30) into (A=P(1 +\frac{r}{n})^{nt}). First, calculate (\frac{r}{n}=\frac{0.0809}{365}\approx0.000221644). Then, calculate (nt=365\times30 = 10950). Next, calculate ((1+\frac{r}{n})^{nt}=(1 + 0.000221644)^{10950}). Using a calculator, ((1 + 0.000221644)^{10950}\approx12.079). Finally, calculate (A=247500\times12.079).

Step3: Calculate the final amount

(A=247500\times12.079 = 247500\times(12+0.079)=247500\times12+247500\times0.079) (247500\times12 = 2970000) and (247500\times0.079=19552.5) (A=2970000 + 19552.5=$2989552.5)

Answer:

($2989552.50)