Let’s analyze and solve the two problems from the uploaded image.

1. Simple Interest Problem

Question: If you put $200 in a savings account that paid 5.5% simple interest each year, how much interest would you earn in five years?

The formula for simple interest is:
$I = P \cdot r \cdot t$
Where:

• $I$ = Interest
• $P$ = Principal amount ($200)
• $r$ = Annual interest rate (5.5% or 0.055)
• $t$ = Time in years (5 years)

$I = 200 \cdot 0.055 \cdot 5 = 55$

Answer: The interest earned in five years is $55.

2. Compound Interest Problem

Question: If you put $150 in a savings account that paid 6% compounded yearly, how much interest would you earn in five years?

The formula for compound interest is:
$A = P \cdot (1 + r)^t$
Where:

• $A$ = Total amount after interest
• $P$ = Principal amount ($150)
• $r$ = Annual interest rate (6% or 0.06)
• $t$ = Time in years (5 years)

The interest earned is calculated as: $\text{Interest} = A - P$

First, calculate $A$:
$A = 150 \cdot (1 + 0.06)^5 = 150 \cdot (1.3382255776) \approx 200.73$

Then, calculate the interest:
$\text{Interest} = 200.73 - 150 = 50.73$

Answer: The interest earned in five years is approximately $50.73.

Would you like a detailed breakdown of either calculation?

Here are 5 related questions to practice further:

1. What would be the total amount after five years for each scenario?
2. How does increasing the interest rate to 7% affect the compound interest in the second problem?
3. What happens if the compound interest is compounded monthly instead of yearly?
4. How much simple interest is earned if the principal is doubled in the first problem?
5. What is the difference between simple and compound interest after 10 years for the same principal and rate?

Tip:

For compound interest, the frequency of compounding (e.g., yearly, monthly) significantly impacts the total interest earned over time. Always check the compounding period!