a customer uses a store credit card to purchase a boat for $10,500. the store credit card offers an annual…

a customer uses a store credit card to purchase a boat for $10,500. the store credit card offers an annual interest rate, compounded continuously, of 18.99% with no payments due for the first two years. if no payments are made for the two years, what will be the balance on the card, rounded to the nearest penny? $12,679.59 $12,695.85 $15,311.62 $15,350.92

a customer uses a store credit card to purchase a boat for $10,500. the store credit card offers an annual interest rate, compounded continuously, of 18.99% with no payments due for the first two years. if no payments are made for the two years, what will be the balance on the card, rounded to the nearest penny? $12,679.59 $12,695.85 $15,311.62 $15,350.92

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.

Step2: Convert the interest rate to decimal

The annual interest rate $r = 18.99%=0.1899$. The principal amount $P=$10500$ and the time $t = 2$ years.

Step3: Substitute values into the formula

$A=10500\times e^{0.1899\times2}$. First, calculate the exponent: $0.1899\times2 = 0.3798$. Then, find $e^{0.3798}$. Using a calculator, $e^{0.3798}\approx1.461992$. Now, multiply by the principal: $A = 10500\times1.461992\approx15350.92$.

Answer:

D. $15,350.92$