Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Suppose that $10,000 is invested and at the end of 5 years, the value of the account is $13,771.28. Use the model A=Pe^(rt) to determine the average rate of return r under continuous compounding.

Suppose that $10,000 \$ 10,000 is invested and at the end of 55 years, the value of the account is $13,771.28 \$ 13,771.28 . Use the model A=Pert A=P e^{r t} to determine the average rate of return r r under continuous compounding.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Compound interestright chevron icon

Full solution

Q. Suppose that $10,000 \$ 10,000 is invested and at the end of 55 years, the value of the account is $13,771.28 \$ 13,771.28 . Use the model A=Pert A=P e^{r t} to determine the average rate of return r r under continuous compounding.
  1. Isolate erte^{rt}: We have the formula for continuous compounding: A=PertA = Pe^{rt}. Here, A=$13,771.28A = \$13,771.28, P=$10,000P = \$10,000, and t=5t = 5 years. We need to find rr.
  2. Calculate ln⁡(1.377128)\ln(1.377128): First, divide both sides of the equation by PP to isolate erte^{rt}. So, ert=AP=$(13,771.28)$(10,000)=1.377128e^{rt} = \frac{A}{P} = \frac{\$(13,771.28)}{\$(10,000)} = 1.377128.
  3. Simplify to rtrt: Now, take the natural logarithm (ln⁡\ln) of both sides to get rid of the exponent.ln⁡(ert)=ln⁡(1.377128)\ln(e^{rt}) = \ln(1.377128).
  4. Solve for rr: Since ln⁡(e(rt))\ln(e^{(rt)}) simplifies to rtrt, we have rt=ln⁡(1.377128)rt = \ln(1.377128).\newlineCalculate ln⁡(1.377128)\ln(1.377128) using a calculator.\newlinert=ln⁡(1.377128)≈0.319rt = \ln(1.377128) \approx 0.319.
  5. Calculate rr: Finally, divide both sides by tt to solve for rr.r=rtt=0.3195r = \frac{rt}{t} = \frac{0.319}{5}.
  6. Calculate r: Finally, divide both sides by t to solve for r.\newliner=rtt=0.3195r = \frac{rt}{t} = \frac{0.319}{5}.Calculate r.\newliner≈0.3195≈0.0638r \approx \frac{0.319}{5} \approx 0.0638 or 6.38%6.38\%.

More problems from Compound interest

Question
Johnny bought an oil painting originally priced at $80 but on sale for 5050% off. After 1010% sales tax, what was the total cost?\newline`$`____
Get tutor helpright-arrow

Posted 4 months ago

Question
It costs `$40` to buy 44 ironing boards. If the ironing boards all have the same price, how much does it cost to buy 11 ironing board? ` $`_____
Get tutor helpright-arrow

Posted 7 months ago

Question
Whitney buys a lamp online for $93\$93. If shipping and handling are an additional 10%10\% of the price, how much shipping and handling will Whitney pay? \newline $\$ _____\_\_\_\_\_
Get tutor helpright-arrow

Posted 8 months ago

Question
A 99-foot roll of plastic wrap costs $5.40\$5.40. What is the price per inch? \newline $\$ _____
Get tutor helpright-arrow

Posted 7 months ago

Question
A store purchased canoes for $300\$300 and sold them for $435\$435. What percentage is the mark-up? \newlineWrite your answer using a percent sign (%\%). \newline _____
Get tutor helpright-arrow

Posted 7 months ago

Question
A ceramic vase was originally priced at $100\$100 but went on sale for 50%50\% off. If Ernesto bought the ceramic vase and paid 12%12\% sales tax, how much did he pay in total? \newline $\$ ____
Get tutor helpright-arrow

Posted 7 months ago

Question
A 1212-foot roll of aluminum foil costs $7.20\$7.20. What is the price per inch?
Get tutor helpright-arrow

Posted 9 months ago

Question
A 1515-foot roll of paper towel costs $9.75\$9.75. What is the price per inch?
Get tutor helpright-arrow

Posted 7 months ago

Question
A 2020-foot roll of ribbon costs $8.00\$8.00. What is the price per inch?
Get tutor helpright-arrow

Posted 9 months ago

Question
A 66-foot roll of fabric costs $4.50\$4.50. What is the price per inch? \newline $\$ ______
Get tutor helpright-arrow

Posted 7 months ago

View all (39)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant