Name: 16. You deposit $$ \$ 1200 $$ in an account that earns simple interest. After 42 months, the account earns $$ \$ 96.60 $$ in interest. What is the annual interest rate to the nearest tenth of a percent? a. $$ 1.0 \% $$ b. $$ 2.3 \% $$ c. $$ 35.0 \% $$ d. $$ 0.8 \% $$

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UpStudy AI · Accepted Answer

To find the annual interest rate, we can use the formula for simple interest:

$$ I = P \times r \times t $$

where:
- $$ I $$ is the interest earned,
- $$ P $$ is the principal amount (initial deposit),
- $$ r $$ is the annual interest rate,
- $$ t $$ is the time in years.

Given:
- $$ P = \$1200 $$,
- $$ I = \$96.60 $$,
- $$ t = 42 $$ months = $$ \frac{42}{12} $$ years.

We can rearrange the formula to solve for the annual interest rate $$ r $$:

$$ r = \frac{I}{P \times t} $$

Substitute the given values into the formula and calculate the annual interest rate.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{96.6}{\left(1200\left(\frac{42}{12}\right)\right)}$$
- step1: Remove the parentheses:
  $$\frac{96.6}{1200\left(\frac{42}{12}\right)}$$
- step2: Reduce the fraction:
  $$\frac{96.6}{1200\times \frac{7}{2}}$$
- step3: Multiply the numbers:
  $$\frac{96.6}{4200}$$
- step4: Convert the expressions:
  $$\frac{\frac{483}{5}}{4200}$$
- step5: Multiply by the reciprocal:
  $$\frac{483}{5}\times \frac{1}{4200}$$
- step6: Reduce the numbers:
  $$\frac{23}{5}\times \frac{1}{200}$$
- step7: Multiply the fractions:
  $$\frac{23}{5\times 200}$$
- step8: Multiply:
  $$\frac{23}{1000}$$
The annual interest rate is $$0.023$$ or $$2.3\%$$.

Therefore, the correct answer is b. $$2.3\%$$.
The annual interest rate is $$2.3\%$$. Therefore, the correct answer is b. $$2.3\%$$.

Name:
16. You deposit in an account that earns simple
interest. After 42 months, the account earns
in interest. What is the annual interest rate to the
nearest tenth of a percent?
a.
b.
c.
d.

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Name: 16. You deposit in an account that earns simple interest. After 42 months, the account earns in interest. What is the annual interest rate to the nearest tenth of a percent? a. b. c. d.