Question

a certain loan program offers an interest rate of 9.5% per year, compounded continuously. assuming no payments are made, how much would be owed after two years on a loan of $1700? do not round any intermediate computations, and round your answer to the nearest cent.

Explanation:

Step1: Recall the formula for continuous compounding

The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $t$ is the time in years, and $e$ is the base of the natural logarithm.
Here, $P = 1700$, $r = 0.095$ (since $9.5\%=0.095$), and $t = 2$.

Step2: Substitute the values into the formula

Substitute $P = 1700$, $r = 0.095$, and $t = 2$ into the formula:
$A=1700\times e^{0.095\times2}$
First, calculate the exponent: $0.095\times2 = 0.19$
So, $A = 1700\times e^{0.19}$

Step3: Calculate the value of $e^{0.19}$ and then multiply by 1700

We know that $e^{0.19}\approx1.2092$ (using a calculator for the exponential function).
Then, $A = 1700\times1.2092$
$A\approx1700\times1.2092 = 2055.64$

Answer:

$\$2055.64$