a college student plans to take out a $6,000 loan to cover the cost of purchasing a used car. if the loan…
a college student plans to take out a $6,000 loan to cover the cost of purchasing a used car. if the loan has a 6% annual interest rate compounded continuously, with no payments due for the first two years. the student will pay off the loan with a lump sum after 15 months. determine how much interest will be owed if the student pays off the loan after 15 months.\n$565.05\n$467.30\n$8,757.62\n$6,467.30
Answer
Explanation:
Step1: Identify the continuous - compounding formula
The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Here, $P=$6000$, $r = 0.06$, and $t=\frac{15}{12}=1.25$ years.
Step2: Calculate the final amount $A$
Substitute the values into the formula: $A = 6000\times e^{0.06\times1.25}$. First, calculate the exponent: $0.06\times1.25 = 0.075$. Then, find $e^{0.075}\approx1.07788$. So, $A = 6000\times1.07788=$6467.30$.
Step3: Calculate the interest
The interest $I$ is the final amount minus the principal amount. So, $I=A - P$. Substitute $A = 6467.30$ and $P = 6000$ into the formula: $I=6467.30 - 6000=$467.30$.
Answer:
$467.30$