Question

find the compound amount for the deposit and the amount of interest earned. $16,000 at 5% compounded monthly for 13 years. the compound amount after 13 years is $ (do not round until the final answer. then round to the nearest cent as needed.)

Explanation:

Step1: Identify the 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 form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Convert the given values to the appropriate form

Given $P=\$16000$, $r = 5\%=0.05$, $n = 12$ (compounded monthly), and $t = 13$ years.

Step3: Substitute the values into the formula

$A=16000(1 +\frac{0.05}{12})^{12\times13}$.
First, calculate the value inside the parentheses: $\frac{0.05}{12}\approx0.004167$, then $1+\frac{0.05}{12}=1 + 0.004167=1.004167$.
Next, calculate the exponent: $12\times13 = 156$.
So, $A = 16000\times(1.004167)^{156}$.
Using a calculator, $(1.004167)^{156}\approx1.90791$.
Then $A=16000\times1.90791=\$30526.56$.

Answer:

$30526.56$