Question

suppose youre offered the following two accounts to invest $10,000 for 25 years: 9% simple interest and 8% interest compounded monthly. which is the best choice? part 1 of 3 the future value of $10,000 using 9% simple interest is $32500.00. round your answer to the nearest cent. do not round any intermediate steps. alternate answer: the future value of $10,000 using 9% simple interest is $32,500. part: 1 / 3 part 2 of 3 the future value of $10,000 using 8% interest compounded monthly is $. round your answer to the nearest cent. do not round any intermediate steps.

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.
Here, $P=\$10000$, $r = 0.08$, $n=12$ (compounded monthly), and $t = 25$.

Step2: Substitute values into formula

$A=10000(1 +\frac{0.08}{12})^{12\times25}$
First, calculate the value inside the parentheses: $\frac{0.08}{12}\approx0.006667$, then $1+\frac{0.08}{12}=1 + 0.006667=1.006667$.
Next, calculate the exponent: $12\times25 = 300$.
So, $A = 10000\times(1.006667)^{300}$.

Step3: Calculate the final value

Using a calculator, $(1.006667)^{300}\approx7.299718$.
Then $A=10000\times7.299718=\$72997.18$

Answer:

$72997.18$