Compound Interest worksheet with eight problems for students to solve, including calculations for time, interest, and investment amounts with quarterly compounding.
Worksheet titled "Compound Interest" with eight math problems involving compound interest calculations, featuring a colorful turtle wearing a Santa hat in the top right corner.
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Show Answer Key & Explanations
Step-by-step solution for: Money And Consumer Math Worksheets pdf | Math Champions
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Show Answer Key & Explanations
Step-by-step solution for: Money And Consumer Math Worksheets pdf | Math Champions
Here are the step-by-step solutions for each problem on the worksheet.
The Formula:
For all these problems, we use the compound interest formula:
$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$
* $P$: Principal (starting money)
* $r$: Annual interest rate (as a decimal)
* $n$: Number of times compounded per year (Quarterly means $n=4$)
* $t$: Time in years
* $A$: Final Amount (Total balance)
* Interest ($I$): $A - P$
---
* Given: $P = \$791$, Rate $= 8\%$ ($0.08$), Compounded Quarterly ($n=4$), Interest Earned $= \$481.27$.
* Step 1: Find the Total Amount ($A$).
$$A = 791 + 481.27 = \$1,272.27$$
* Step 2: Set up the equation.
$$1272.27 = 791 \left(1 + \frac{0.08}{4}\right)^{4t}$$
$$1272.27 = 791 (1.02)^{4t}$$
* Step 3: Solve for $t$.
Divide by 791:
$$1.6084 \approx (1.02)^{4t}$$
Take the natural log ($\ln$) of both sides:
$$\ln(1.6084) = 4t \cdot \ln(1.02)$$
$$0.4752 \approx 4t \cdot 0.0198$$
$$0.4752 \approx 0.0792t$$
$$t \approx 6$$
Answer: 6 years
---
* Given: $P = \$626$, Rate $= 10\%$ ($0.10$), Time $= 8$ years, Compounded Quarterly ($n=4$).
* Step 1: Calculate the Total Amount ($A$).
$$A = 626 \left(1 + \frac{0.10}{4}\right)^{4 \times 8}$$
$$A = 626 (1.025)^{32}$$
$$A = 626 (2.20375...)$$
$$A \approx \$1,379.55$$
* Step 2: Calculate the Interest.
$$Interest = A - P$$
$$Interest = 1379.55 - 626 = \$753.55$$
Answer: $753.55
---
* Given: $P = \$747$, Rate $= 4\%$ ($0.04$), Time $= 5$ years, Compounded Quarterly ($n=4$).
* Step 1: Calculate the Total Amount ($A$).
$$A = 747 \left(1 + \frac{0.04}{4}\right)^{4 \times 5}$$
$$A = 747 (1.01)^{20}$$
$$A = 747 (1.22019...)$$
$$A \approx \$911.48$$
Answer: $911.48
---
* Given: $P = \$500$, Rate $= 7\%$ ($0.07$), Time $= 8$ years, Compounded Quarterly ($n=4$).
* Step 1: Calculate the Total Amount ($A$).
$$A = 500 \left(1 + \frac{0.07}{4}\right)^{4 \times 8}$$
$$A = 500 (1.0175)^{32}$$
$$A = 500 (1.7449...)$$
$$A \approx \$872.47$$
* Step 2: Calculate the Interest.
$$Interest = 872.47 - 500 = \$372.47$$
Answer: $372.47
---
* Given: $P = \$683$, Rate $= 3\%$ ($0.03$), Time $= 9$ years, Compounded Quarterly ($n=4$).
* Step 1: Calculate the Total Amount ($A$).
$$A = 683 \left(1 + \frac{0.03}{4}\right)^{4 \times 9}$$
$$A = 683 (1.0075)^{36}$$
$$A = 683 (1.3086...)$$
$$A \approx \$893.80$$
* Step 2: Calculate the Interest.
$$Interest = 893.80 - 683 = \$210.80$$
Answer: $210.80
---
* Given: $P = \$986$, $A = \$1,215.45$, Time $= 7$ years, Compounded Quarterly ($n=4$).
* Step 1: Set up the equation.
$$1215.45 = 986 \left(1 + \frac{r}{4}\right)^{4 \times 7}$$
$$1215.45 = 986 \left(1 + \frac{r}{4}\right)^{28}$$
* Step 2: Isolate the parenthesis.
Divide by 986:
$$1.2327 \approx \left(1 + \frac{r}{4}\right)^{28}$$
* Step 3: Remove the exponent.
Raise both sides to the power of $\frac{1}{28}$:
$$(1.2327)^{\frac{1}{28}} = 1 + \frac{r}{4}$$
$$1.0075 \approx 1 + \frac{r}{4}$$
* Step 4: Solve for $r$.
Subtract 1:
$$0.0075 = \frac{r}{4}$$
Multiply by 4:
$$r = 0.03$$
Convert to percentage: $3\%$
Answer: 3%
---
* Given: $A = \$357.15$, Rate $= 5\%$ ($0.05$), Time $= 8$ years, Compounded Quarterly ($n=4$).
* Step 1: Set up the equation.
$$357.15 = P \left(1 + \frac{0.05}{4}\right)^{4 \times 8}$$
$$357.15 = P (1.0125)^{32}$$
* Step 2: Calculate the multiplier.
$$(1.0125)^{32} \approx 1.48813$$
* Step 3: Solve for $P$.
$$357.15 = P (1.48813)$$
$$P = \frac{357.15}{1.48813}$$
$$P \approx 240.00$$
Answer: $240.00
---
* Given: $P = \$578$, Interest Received $= \$325.96$, Rate $= 5\%$ ($0.05$), Compounded Quarterly ($n=4$).
* Step 1: Find the Total Amount ($A$).
$$A = 578 + 325.96 = \$903.96$$
* Step 2: Set up the equation.
$$903.96 = 578 \left(1 + \frac{0.05}{4}\right)^{4t}$$
$$903.96 = 578 (1.0125)^{4t}$$
* Step 3: Solve for $t$.
Divide by 578:
$$1.5639 \approx (1.0125)^{4t}$$
Take the natural log ($\ln$):
$$\ln(1.5639) = 4t \cdot \ln(1.0125)$$
$$0.4472 \approx 4t \cdot 0.01242$$
$$0.4472 \approx 0.04968t$$
$$t \approx 9$$
Answer: 9 years
The Formula:
For all these problems, we use the compound interest formula:
$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$
* $P$: Principal (starting money)
* $r$: Annual interest rate (as a decimal)
* $n$: Number of times compounded per year (Quarterly means $n=4$)
* $t$: Time in years
* $A$: Final Amount (Total balance)
* Interest ($I$): $A - P$
---
1. How long was the period of time?
* Given: $P = \$791$, Rate $= 8\%$ ($0.08$), Compounded Quarterly ($n=4$), Interest Earned $= \$481.27$.
* Step 1: Find the Total Amount ($A$).
$$A = 791 + 481.27 = \$1,272.27$$
* Step 2: Set up the equation.
$$1272.27 = 791 \left(1 + \frac{0.08}{4}\right)^{4t}$$
$$1272.27 = 791 (1.02)^{4t}$$
* Step 3: Solve for $t$.
Divide by 791:
$$1.6084 \approx (1.02)^{4t}$$
Take the natural log ($\ln$) of both sides:
$$\ln(1.6084) = 4t \cdot \ln(1.02)$$
$$0.4752 \approx 4t \cdot 0.0198$$
$$0.4752 \approx 0.0792t$$
$$t \approx 6$$
Answer: 6 years
---
2. How much interest will you receive?
* Given: $P = \$626$, Rate $= 10\%$ ($0.10$), Time $= 8$ years, Compounded Quarterly ($n=4$).
* Step 1: Calculate the Total Amount ($A$).
$$A = 626 \left(1 + \frac{0.10}{4}\right)^{4 \times 8}$$
$$A = 626 (1.025)^{32}$$
$$A = 626 (2.20375...)$$
$$A \approx \$1,379.55$$
* Step 2: Calculate the Interest.
$$Interest = A - P$$
$$Interest = 1379.55 - 626 = \$753.55$$
Answer: $753.55
---
3. What will the balance be at the end of five years?
* Given: $P = \$747$, Rate $= 4\%$ ($0.04$), Time $= 5$ years, Compounded Quarterly ($n=4$).
* Step 1: Calculate the Total Amount ($A$).
$$A = 747 \left(1 + \frac{0.04}{4}\right)^{4 \times 5}$$
$$A = 747 (1.01)^{20}$$
$$A = 747 (1.22019...)$$
$$A \approx \$911.48$$
Answer: $911.48
---
4. How much interest does the investment earn?
* Given: $P = \$500$, Rate $= 7\%$ ($0.07$), Time $= 8$ years, Compounded Quarterly ($n=4$).
* Step 1: Calculate the Total Amount ($A$).
$$A = 500 \left(1 + \frac{0.07}{4}\right)^{4 \times 8}$$
$$A = 500 (1.0175)^{32}$$
$$A = 500 (1.7449...)$$
$$A \approx \$872.47$$
* Step 2: Calculate the Interest.
$$Interest = 872.47 - 500 = \$372.47$$
Answer: $372.47
---
5. How much interest will you pay?
* Given: $P = \$683$, Rate $= 3\%$ ($0.03$), Time $= 9$ years, Compounded Quarterly ($n=4$).
* Step 1: Calculate the Total Amount ($A$).
$$A = 683 \left(1 + \frac{0.03}{4}\right)^{4 \times 9}$$
$$A = 683 (1.0075)^{36}$$
$$A = 683 (1.3086...)$$
$$A \approx \$893.80$$
* Step 2: Calculate the Interest.
$$Interest = 893.80 - 683 = \$210.80$$
Answer: $210.80
---
6. What was the interest rate?
* Given: $P = \$986$, $A = \$1,215.45$, Time $= 7$ years, Compounded Quarterly ($n=4$).
* Step 1: Set up the equation.
$$1215.45 = 986 \left(1 + \frac{r}{4}\right)^{4 \times 7}$$
$$1215.45 = 986 \left(1 + \frac{r}{4}\right)^{28}$$
* Step 2: Isolate the parenthesis.
Divide by 986:
$$1.2327 \approx \left(1 + \frac{r}{4}\right)^{28}$$
* Step 3: Remove the exponent.
Raise both sides to the power of $\frac{1}{28}$:
$$(1.2327)^{\frac{1}{28}} = 1 + \frac{r}{4}$$
$$1.0075 \approx 1 + \frac{r}{4}$$
* Step 4: Solve for $r$.
Subtract 1:
$$0.0075 = \frac{r}{4}$$
Multiply by 4:
$$r = 0.03$$
Convert to percentage: $3\%$
Answer: 3%
---
7. What was the principal?
* Given: $A = \$357.15$, Rate $= 5\%$ ($0.05$), Time $= 8$ years, Compounded Quarterly ($n=4$).
* Step 1: Set up the equation.
$$357.15 = P \left(1 + \frac{0.05}{4}\right)^{4 \times 8}$$
$$357.15 = P (1.0125)^{32}$$
* Step 2: Calculate the multiplier.
$$(1.0125)^{32} \approx 1.48813$$
* Step 3: Solve for $P$.
$$357.15 = P (1.48813)$$
$$P = \frac{357.15}{1.48813}$$
$$P \approx 240.00$$
Answer: $240.00
---
8. For how long did you invest the principal?
* Given: $P = \$578$, Interest Received $= \$325.96$, Rate $= 5\%$ ($0.05$), Compounded Quarterly ($n=4$).
* Step 1: Find the Total Amount ($A$).
$$A = 578 + 325.96 = \$903.96$$
* Step 2: Set up the equation.
$$903.96 = 578 \left(1 + \frac{0.05}{4}\right)^{4t}$$
$$903.96 = 578 (1.0125)^{4t}$$
* Step 3: Solve for $t$.
Divide by 578:
$$1.5639 \approx (1.0125)^{4t}$$
Take the natural log ($\ln$):
$$\ln(1.5639) = 4t \cdot \ln(1.0125)$$
$$0.4472 \approx 4t \cdot 0.01242$$
$$0.4472 \approx 0.04968t$$
$$t \approx 9$$
Answer: 9 years
Parent Tip: Review the logic above to help your child master the concept of consumer math worksheet for high school.
