Calculating Interest on Savings

You deposit 500 dollars in a savings account that pays 4% simple interest per year. How much interest will you earn after 3 years?

Identify the values: $P = 500$, $r = 4\% = 0.04$, $t = 3$ = Values identified

Write the formula: $I = P \times r \times t$ = Formula ready

Substitute the values: $I = 500 \times 0.04 \times 3$ = Values substituted

Calculate step by step: $I = 500 \times 0.04 = 20$, then $20 \times 3 = 60$ = $I = 60$

Answer: You will earn 60 dollars in interest after 3 years.

Finding Total Amount Owed on a Loan

Maria borrows 2000 dollars at 6% simple interest for 4 years. How much will she pay back in total?

Identify the values: $P = 2000$, $r = 6\% = 0.06$, $t = 4$ = Values identified

Calculate the interest: $I = 2000 \times 0.06 \times 4 = 480$ = $I = 480$

Find total amount: $A = P + I = 2000 + 480$ = $A = 2480$

Answer: Maria will pay back 2480 dollars in total (2000 dollars principal + 480 dollars interest).

Finding the Interest Rate

James invested 1500 dollars and earned 225 dollars in interest over 3 years. What was the annual interest rate?

Identify known values: $P = 1500$, $I = 225$, $t = 3$, $r = ?$ = Need to find rate

Rearrange the formula: $I = P \times r \times t \Rightarrow r = \frac{I}{P \times t}$ = Formula rearranged

Substitute and solve: $r = \frac{225}{1500 \times 3} = \frac{225}{4500} = 0.05$ = $r = 0.05$

Convert to percentage: $r = 0.05 \times 100\% = 5\%$ = Rate is 5%

Answer: The annual interest rate was 5%.

Finding Time to Reach a Goal

You want to earn 120 dollars in interest on a 1000 dollar deposit at 4% simple interest. How long will it take?

Identify known values: $P = 1000$, $I = 120$, $r = 0.04$, $t = ?$ = Need to find time

Rearrange the formula: $I = P \times r \times t \Rightarrow t = \frac{I}{P \times r}$ = Formula rearranged

Substitute and solve: $t = \frac{120}{1000 \times 0.04} = \frac{120}{40} = 3$ = $t = 3$

Answer: It will take 3 years to earn 120 dollars in interest.

Mistake: Forgetting to convert percentage to decimal

Why: Using $r = 5$ instead of $r = 0.05$ gives an answer 100 times too large.

Correct: Always divide the percentage by 100: $5\% = 5 \div 100 = 0.05$

Mistake: Using months instead of years for time

Why: The formula uses annual rate, so time must be in years.

Correct: Convert months to years: 6 months = $\frac{6}{12} = 0.5$ years

Mistake: Confusing interest with total amount

Why: Interest ($I$) is just what you earn/owe. Total amount ($A$) includes the principal.

Correct: Total amount = Principal + Interest: $A = P + I$

Savings Account Growth

Banks pay you interest for keeping money in savings accounts. Simple interest shows the basic growth pattern.

A savings account with 800 dollars at 3% for 2 years earns $800 \times 0.03 \times 2 = 48$ dollars.

Car Loans

Many car loans use simple interest. Understanding this helps you know exactly how much extra you will pay.

A 10000 dollar car loan at 7% for 5 years means paying $10000 \times 0.07 \times 5 = 3500$ dollars in interest.

Lending Money to Friends

Even informal loans can involve interest. Understanding simple interest helps both parties agree on fair terms.

If you lend 200 dollars to a friend at 2% for 6 months, the interest is $200 \times 0.02 \times 0.5 = 2$ dollars.

Q: What is the difference between simple and compound interest?

A: Simple interest is calculated only on the original principal. Compound interest is calculated on the principal PLUS any interest already earned, so it grows faster over time.

Q: Why do I need to convert percentages to decimals?

A: Percentages are a way to express parts per hundred. To use them in calculations, we convert to decimals: $5\% = \frac{5}{100} = 0.05$. This ensures the math works correctly.

Q: Can time be less than one year?

A: Yes! Convert months to years by dividing by 12. For example, 6 months = 0.5 years, 3 months = 0.25 years.