13) Ms. Timarky deposits $$ \$ 300 $$ in an account that earns simple interest at an annual rate of $$ 2 \% $$. Ms. Waugh deposits $$ \$ 300 $$ in an account that earns $$ 2 \% $$ interest and is compounded annually. After 5 years, who has more money in their account and why?

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UpStudy AI · Accepted Answer

To determine who has more money in their account after 5 years—**Ms. Timarky** with simple interest or **Ms. Waugh** with compound interest—we can calculate the future value of each account.

### **1. Simple Interest Calculation (Ms. Timarky)**

The formula for **simple interest** is:

$$
A = P(1 + rt)
$$

Where:
- $$ P = \$300 $$ (principal)
- $$ r = 2\% = 0.02 $$ (annual interest rate)
- $$ t = 5 $$ years

**Calculation:**

$$
A = 300 \times (1 + 0.02 \times 5) = 300 \times (1 + 0.10) = 300 \times 1.10 = \$330
$$

### **2. Compound Interest Calculation (Ms. Waugh)**

The formula for **compound interest** is:

$$
A = P(1 + r)^t
$$

Where the variables are the same as above.

**Calculation:**

First, compute $$ (1 + 0.02)^5 $$:

$$
(1.02)^5 \approx 1.10408
$$

Then,

$$
A = 300 \times 1.10408 \approx \$331.23
$$

### **Conclusion**

After 5 years:
- **Ms. Timarky** will have **\$330**.
- **Ms. Waugh** will have approximately **\$331.23**.

**Ms. Waugh** has more money in her account because **compound interest** allows the interest to earn interest each year, leading to a slightly higher amount compared to simple interest.
After 5 years, Ms. Waugh has more money in her account because compound interest earns interest on both the principal and the accumulated interest, resulting in a higher total than simple interest.

Ms. Timarky deposits in an account that earns simple interest at an annual rate of . Ms. Waugh deposits in an account that earns interest and is compounded annually. After 5 years, who has more money in their account and why?

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