suppose youre offered the following two accounts to invest $10,000 for 20 years: 16% simple interest and 4%…
suppose youre offered the following two accounts to invest $10,000 for 20 years: 16% simple interest and 4% interest compounded monthly. which is the best choice? part 1 of 3 the future value of $10,000 using 16% simple interest is $42000.00. round your answer to the nearest cent. do not round any intermediate steps. alternate answer: the future value of $10,000 using 16% simple interest is $42,000. part: 1 / 3 part 2 of 3 the future value of $10,000 using 4% interest compounded monthly is $ . round your answer to the nearest cent. do not round any intermediate steps.
Answer
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=$10000$, $r = 0.04$, $n=12$ (compounded monthly), and $t = 20$.
Step2: Substitute values into the formula
$A=10000(1 +\frac{0.04}{12})^{12\times20}$. First, calculate the value inside the parentheses: $\frac{0.04}{12}\approx0.003333$. Then $1+\frac{0.04}{12}=1 + 0.003333=1.003333$. Next, calculate the exponent: $12\times20 = 240$. So, $A = 10000\times(1.003333)^{240}$. Using a calculator, $(1.003333)^{240}\approx2.21964$. Then $A=10000\times2.21964=$22196.40$.
Answer:
$22196.40$