Question If Karla's $$ \$ 10,000 $$ investment grows to $$ \$ 11,149.48 $$ in 5 years, what is her interest rate compounded annually? Round your answer to one decimal place.

Question

UpStudy AI · Accepted Answer

1. Write the compound interest formula:
   $$
   A = P(1+r)^n
   $$
   where:
   - $$ A = \$11,149.48 $$ (future value),
   - $$ P = \$10,000 $$ (principal),
   - $$ r $$ is the annual interest rate,
   - $$ n = 5 $$ years.

2. Substitute the given values into the formula:
   $$
   11149.48 = 10000(1+r)^5
   $$

3. Divide both sides by $$ 10000 $$ to isolate $$(1+r)^5$$:
   $$
   (1+r)^5 = \frac{11149.48}{10000} = 1.114948
   $$

4. Take the fifth root of both sides to solve for $$ 1+r $$:
   $$
   1+r = \sqrt[5]{1.114948} = (1.114948)^{\frac{1}{5}}
   $$

5. Solve for $$ r $$:
   $$
   r = (1.114948)^{\frac{1}{5}} - 1
   $$
   Using a calculator,
   $$
   (1.114948)^{\frac{1}{5}} \approx 1.022
   $$
   Thus,
   $$
   r \approx 1.022 - 1 = 0.022
   $$

6. Convert the decimal to a percentage:
   $$
   0.022 \times 100\% \approx 2.2\%
   $$

The annual interest rate is approximately $$2.2\%$$.
The annual interest rate is approximately 2.2%.

Question
If Karla’s investment grows to in 5 years, what is her interest rate compounded annually? Round your
answer to one decimal place.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Pre Algebra Questions

Question If Karla’s investment grows to in 5 years, what is her interest rate compounded annually? Round your answer to one decimal place.