Simple Interest Math Worksheet with Practice Problems

Problem: Solving Simple Interest Problems

The formula for calculating Simple Interest is:

\[
I = P \times r \times t
\]

Where:
- \( I \) = Interest earned or paid
- \( P \) = Principal amount (initial investment or loan)
- \( r \) = Annual interest rate (in decimal form)
- \( t \) = Time in years

We will solve each problem step by step using this formula.

---

1. How much interest is earned on $2,566.45 at 0.4% for three years?

#### Given:
- \( P = 2,566.45 \)
- \( r = 0.4\% = 0.004 \) (convert percentage to decimal)
- \( t = 3 \)

#### Formula:
\[
I = P \times r \times t
\]

#### Calculation:
\[
I = 2,566.45 \times 0.004 \times 3
\]
\[
I = 2,566.45 \times 0.012
\]
\[
I = 30.7974
\]

#### Answer:
\[
\boxed{30.80}
\]

---

2. You put $8,185.06 into a savings account with an interest rate of 0.7% which earns $14.59 over a period of time. How long was the period of time?

#### Given:
- \( P = 8,185.06 \)
- \( r = 0.7\% = 0.007 \)
- \( I = 14.59 \)

#### Formula:
\[
I = P \times r \times t
\]

Rearrange to solve for \( t \):
\[
t = \frac{I}{P \times r}
\]

#### Calculation:
\[
t = \frac{14.59}{8,185.06 \times 0.007}
\]
\[
t = \frac{14.59}{57.29542}
\]
\[
t \approx 0.2546
\]

#### Answer:
\[
\boxed{0.25 \text{ years}}
\]

---

3. If a loan is taken out for $40.54 at 0.9% and costs $1.09, how long was the loan for?

#### Given:
- \( P = 40.54 \)
- \( r = 0.9\% = 0.009 \)
- \( I = 1.09 \)

#### Formula:
\[
I = P \times r \times t
\]

Rearrange to solve for \( t \):
\[
t = \frac{I}{P \times r}
\]

#### Calculation:
\[
t = \frac{1.09}{40.54 \times 0.009}
\]
\[
t = \frac{1.09}{0.36486}
\]
\[
t \approx 3.0
\]

#### Answer:
\[
\boxed{3 \text{ years}}
\]

---

4. You invested $45.12 and received $45.75 after two years. What was the interest rate?

#### Given:
- \( P = 45.12 \)
- \( I = 45.75 - 45.12 = 0.63 \) (Interest earned)
- \( t = 2 \)

#### Formula:
\[
I = P \times r \times t
\]

Rearrange to solve for \( r \):
\[
r = \frac{I}{P \times t}
\]

#### Calculation:
\[
r = \frac{0.63}{45.12 \times 2}
\]
\[
r = \frac{0.63}{90.24}
\]
\[
r \approx 0.007
\]

Convert to percentage:
\[
r = 0.007 \times 100 = 0.7\%
\]

#### Answer:
\[
\boxed{0.7\%}
\]

---

5. What will the final balance be for $370.86 invested at 0.3% for nine years?

#### Given:
- \( P = 370.86 \)
- \( r = 0.3\% = 0.003 \)
- \( t = 9 \)

#### Formula for Final Balance:
\[
\text{Final Balance} = P + I
\]
\[
I = P \times r \times t
\]

#### Calculate Interest:
\[
I = 370.86 \times 0.003 \times 9
\]
\[
I = 370.86 \times 0.027
\]
\[
I = 9.99342
\]

#### Calculate Final Balance:
\[
\text{Final Balance} = P + I
\]
\[
\text{Final Balance} = 370.86 + 9.99342
\]
\[
\text{Final Balance} \approx 380.85
\]

#### Answer:
\[
\boxed{380.85}
\]

---

6. How much interest is earned on $128.51 at 1.5% for four years?

#### Given:
- \( P = 128.51 \)
- \( r = 1.5\% = 0.015 \)
- \( t = 4 \)

#### Formula:
\[
I = P \times r \times t
\]

#### Calculation:
\[
I = 128.51 \times 0.015 \times 4
\]
\[
I = 128.51 \times 0.06
\]
\[
I = 7.7106
\]

#### Answer:
\[
\boxed{7.71}
\]

---

7. If you received $3.33 on $61.66 invested at a rate of 0.9%, for how long did you invest the principal?

#### Given:
- \( P = 61.66 \)
- \( r = 0.9\% = 0.009 \)
- \( I = 3.33 \)

#### Formula:
\[
I = P \times r \times t
\]

Rearrange to solve for \( t \):
\[
t = \frac{I}{P \times r}
\]

#### Calculation:
\[
t = \frac{3.33}{61.66 \times 0.009}
\]
\[
t = \frac{3.33}{0.55494}
\]
\[
t \approx 6.0
\]

#### Answer:
\[
\boxed{6 \text{ years}}
\]

---

8. How much interest does a $1,149.38 investment earn at 5% over three years?

#### Given:
- \( P = 1,149.38 \)
- \( r = 5\% = 0.05 \)
- \( t = 3 \)

#### Formula:
\[
I = P \times r \times t
\]

#### Calculation:
\[
I = 1,149.38 \times 0.05 \times 3
\]
\[
I = 1,149.38 \times 0.15
\]
\[
I = 172.407
\]

#### Answer:
\[
\boxed{172.41}
\]

---

9. You put $2,225.50 into an investment at 1.3% for eight years. What will the balance be at the end of eight years?

#### Given:
- \( P = 2,225.50 \)
- \( r = 1.3\% = 0.013 \)
- \( t = 8 \)

#### Formula for Final Balance:
\[
\text{Final Balance} = P + I
\]
\[
I = P \times r \times t
\]

#### Calculate Interest:
\[
I = 2,225.50 \times 0.013 \times 8
\]
\[
I = 2,225.50 \times 0.104
\]
\[
I = 230.662
\]

#### Calculate Final Balance:
\[
\text{Final Balance} = P + I
\]
\[
\text{Final Balance} = 2,225.50 + 230.662
\]
\[
\text{Final Balance} \approx 2,456.16
\]

#### Answer:
\[
\boxed{2,456.16}
\]

---

10. How much interest is earned on $2,078.24 at 0.6% for eight years?

#### Given:
- \( P = 2,078.24 \)
- \( r = 0.6\% = 0.006 \)
- \( t = 8 \)

#### Formula:
\[
I = P \times r \times t
\]

#### Calculation:
\[
I = 2,078.24 \times 0.006 \times 8
\]
\[
I = 2,078.24 \times 0.048
\]
\[
I = 99.75552
\]

#### Answer:
\[
\boxed{99.76}
\]

---

Final Answers:

1. \(\boxed{30.80}\)
2. \(\boxed{0.25 \text{ years}}\)
3. \(\boxed{3 \text{ years}}\)
4. \(\boxed{0.7\%}\)
5. \(\boxed{380.85}\)
6. \(\boxed{7.71}\)
7. \(\boxed{6 \text{ years}}\)
8. \(\boxed{172.41}\)
9. \(\boxed{2,456.16}\)
10. \(\boxed{99.76}\)