dan borrowed $8000 at a rate of 12.5%, compou...
dan borrowed $8000 at a rate of 12.5%, compounded semiannually. assuming he makes no payments, how much will he owe after 8 years? do not round any intermediate computations, and round your answer to the nearest cent.
Answer
# Explanation:
## Step1: Identify 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 values to appropriate form
Given $P=\$8000$, $r = 12.5\%=0.125$, $n = 2$ (compounded semiannually), and $t = 8$ years.
## Step3: Substitute values into formula
$A=8000(1 +\frac{0.125}{2})^{2\times8}=8000(1 + 0.0625)^{16}$.
## Step4: Calculate the value inside the parentheses
$1+0.0625 = 1.0625$.
## Step5: Calculate the exponentiation
$(1.0625)^{16}\approx2.685063838$.
## Step6: Calculate the final amount
$A = 8000\times2.685063838=\$21480.510704\approx\$21480.51$.
# Answer:
$21480.51$