assignment: applications 2 - 6a\nassignment score: 11.42%\nsave submit assignment for grading\nquestions…
assignment: applications 2 - 6a\nassignment score: 11.42%\nsave submit assignment for grading\nquestions ge6fa02h.ap2 - 6.02\nquestion 2 of 7\ncheck my work\nnote: 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).\nfind the interest earned on a $50,000 deposited for six years at 1\\frac{1}{8}% interest, compounded continuously. round to the nearest cent.
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. The interest earned $I=A - P$. First, convert the interest rate to decimal. The interest rate $r = 1\frac{1}{8}%=\frac{9}{8}% = 0.01125$, $P=$50000$, and $t = 6$ years.
Step2: Calculate the final amount $A$
Substitute the values into the formula $A = Pe^{rt}$. So, $A=50000\times e^{0.01125\times6}$. Calculate $0.01125\times6 = 0.0675$. Then $A = 50000\times e^{0.0675}$. Since $e^{0.0675}\approx1.070$, $A = 50000\times1.070237\approx53511.85$.
Step3: Calculate the interest earned $I$
$I=A - P$. Substitute $A\approx53511.85$ and $P = 50000$ into the formula. $I=53511.85 - 50000=$3511.85$.
Answer:
$$3,511.85$