a college student plans to take out a $6,000 loan to cover the cost of purchasing a used car. the loan has a…

a college student plans to take out a $6,000 loan to cover the cost of purchasing a used car. the loan has a 6% annual interest rate compounded continuously, with no payments due for the first two years. determine the balance due at the end of the first two years. $6,764.98 $5,183.28 $5,637.58 $7,166.65

a college student plans to take out a $6,000 loan to cover the cost of purchasing a used car. the loan has a 6% annual interest rate compounded continuously, with no payments due for the first two years. determine the balance due at the end of the first two years. $6,764.98 $5,183.28 $5,637.58 $7,166.65

Answer

Explanation:

Step1: Identify the 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.

Step2: Convert the interest rate to decimal

The annual interest rate $r = 6%=0.06$, the principal amount $P = 6000$, and the time $t = 2$ years.

Step3: Substitute values into the formula

$A=6000\times e^{0.06\times2}$. First, calculate the exponent: $0.06\times2 = 0.12$. Then, find $e^{0.12}\approx1.127497$. Multiply by the principal: $A = 6000\times1.127497=6764.982\approx6764.98$.

Answer:

A. $6,764.98$