find the interest earned on a $30,000 deposit for six months at 1 1/2% interest, compounded continuously…

find the interest earned on a $30,000 deposit for six months at 1 1/2% interest, compounded continuously. note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).

find the interest earned on a $30,000 deposit for six months at 1 1/2% interest, compounded continuously. note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).

Answer

Explanation:

Step1: Identify the formula for continuous - compounding interest

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. The interest earned $I=A - P$. First, convert the given values: $P = 30000$, $r=\frac{1.5}{100}=0.015$ (since $1\frac{1}{2}%=1.5%$), and $t=\frac{6}{12}=0.5$ years.

Step2: Calculate the final amount $A$

Substitute the values into the formula $A = Pe^{rt}$. So, $A = 30000\times e^{0.015\times0.5}$. Using a calculator, $e^{0.015\times0.5}=e^{0.0075}\approx1.007528$. Then $A = 30000\times1.007528 = 30225.84$.

Step3: Calculate the interest earned $I$

$I=A - P$. Substitute $A = 30225.84$ and $P = 30000$ into the formula. So, $I=30225.84 - 30000=225.84$.

Answer:

225.84