Syed is comparing savings accounts earning simple interest. One savings account (account A) advertises
“Invest with us and your could become at the end of 1 year!” The other savings account (account
B) advertises “Deposit your money here and we guarantee to double your money at the end of 10 years!”
Compare the interest rates of the two accounts. Round to the nearest hundredth of a percent.
Account A earns
Account B earns

Question

Syed is comparing savings accounts earning simple interest. One savings account (account A) advertises
“Invest with us and your

could become

at the end of 1 year!” The other savings account (account
B) advertises “Deposit your money here and we guarantee to double your money at the end of 10 years!”
Compare the interest rates of the two accounts. Round to the nearest hundredth of a percent.
Account A earns
Account B earns

UpStudy AI · Accepted Answer

**Step 1: Account A Calculation**

The simple interest formula is given by:
$$
A = P(1 + rt)
$$
For Account A, the initial amount is $$ P = \$135 $$, the final amount is $$ A = \$145 $$, and the time is $$ t = 1 $$ year. Substituting these values:
$$
145 = 135(1 + r \cdot 1)
$$
Divide both sides by 135:
$$
1 + r = \frac{145}{135} \approx 1.07407
$$
Subtract 1 from both sides to solve for $$ r $$:
$$
r \approx 1.07407 - 1 = 0.07407
$$
Expressed as a percentage:
$$
r \approx 7.41\%
$$

**Step 2: Account B Calculation**

For Account B, the money doubles in 10 years. Using the simple interest formula:
$$
2P = P(1 + r \cdot 10)
$$
Divide both sides by $$ P $$:
$$
2 = 1 + 10r
$$
Subtract 1 from both sides:
$$
10r = 1
$$
Solve for $$ r $$:
$$
r = \frac{1}{10} = 0.10
$$
Expressed as a percentage:
$$
r = 10.00\%
$$

**Final Answer:**

- Account A earns approximately $$ 7.41\% $$ simple interest per year.
- Account B earns $$ 10.00\% $$ simple interest per year.
Account A earns approximately 7.41% simple interest per year, and Account B earns 10.00% simple interest per year.

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