Compound Interest Worksheet 01 Worksheets - Free Printable
Educational worksheet: Compound Interest Worksheet 01 Worksheets. Download and print for classroom or home learning activities.
JPG
363×470
16.7 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1622651
⭐
Show Answer Key & Explanations
Step-by-step solution for: Compound Interest Worksheet 01 Worksheets
▼
Show Answer Key & Explanations
Step-by-step solution for: Compound Interest Worksheet 01 Worksheets
Here are the step-by-step solutions for the compound interest problems on your worksheet.
The formula used for all these problems is:
$$A = P(1 + r)^t$$
* $A$ = The final amount (Total money)
* $P$ = The principal (Starting money)
* $r$ = The interest rate (written as a decimal, e.g., $8\% = 0.08$)
* $t$ = Time in years
***
1. How much interest is earned on a principal of $\$432$ invested at an interest rate of $8\%$ compounded annually for six years?
* Step 1: Identify the values. $P = 432$, $r = 0.08$, $t = 6$.
* Step 2: Plug into the formula to find the Total Amount ($A$).
$$A = 432(1 + 0.08)^6$$
$$A = 432(1.08)^6$$
$$A \approx 432(1.58687)$$
$$A \approx 685.53$$
* Step 3: Calculate the Interest. The question asks for *interest*, not the total.
$$\text{Interest} = \text{Total Amount} - \text{Principal}$$
$$\text{Interest} = 685.53 - 432 = 253.53$$
2. If you borrow $\$501$ at $7\%$ compounded annually for seven years, how much will you pay back by the end of the term?
* Step 1: Identify values. $P = 501$, $r = 0.07$, $t = 7$. "Pay back" means the Total Amount ($A$).
* Step 2: Plug into the formula.
$$A = 501(1 + 0.07)^7$$
$$A = 501(1.07)^7$$
$$A \approx 501(1.60578)$$
$$A \approx 804.50$$
3. How much interest is earned on a principal of $\$542$ invested at an interest rate of $3\%$ compounded annually for five years?
* Step 1: Identify values. $P = 542$, $r = 0.03$, $t = 5$.
* Step 2: Find Total Amount ($A$).
$$A = 542(1 + 0.03)^5$$
$$A = 542(1.03)^5$$
$$A \approx 542(1.15927)$$
$$A \approx 628.33$$
* Step 3: Calculate Interest.
$$\text{Interest} = 628.33 - 542 = 86.33$$
4. You put $\$420$ into a savings account with an interest rate of $8\%$ compounded annually which earns $\$53.80$ over a period of time. How long was the period of time?
* Step 1: Identify values. $P = 420$, $r = 0.08$, Interest $= 53.80$.
* Step 2: Find Total Amount ($A$) first.
$$A = 420 + 53.80 = 473.80$$
* Step 3: Set up the equation and solve for $t$.
$$473.80 = 420(1.08)^t$$
Divide both sides by $420$:
$$1.1281 = (1.08)^t$$
Using logarithms or trial and error:
$1.08^1 = 1.08$
$1.08^2 = 1.166$ (Too high)
Let's check closer to 1.5 years? No, usually these are whole numbers. Let's re-calculate precisely.
$\ln(1.1281) / \ln(1.08) \approx 1.5$ years.
*(Note: In many school contexts, if the answer isn't a whole number, it might be rounded. $1.5$ years is the precise mathematical answer).*
5. If you put $\$345$ in a savings account that pays $5\%$ compounded annually for nine years what is the amount of money you will have at the end of the nine years?
* Step 1: Identify values. $P = 345$, $r = 0.05$, $t = 9$.
* Step 2: Plug into the formula.
$$A = 345(1 + 0.05)^9$$
$$A = 345(1.05)^9$$
$$A \approx 345(1.55133)$$
$$A \approx 535.21$$
6. If you put $\$989$ into a savings account that earns $9\%$ compounded annually, how much interest will you receive at the end of six years?
* Step 1: Identify values. $P = 989$, $r = 0.09$, $t = 6$.
* Step 2: Find Total Amount ($A$).
$$A = 989(1 + 0.09)^6$$
$$A = 989(1.09)^6$$
$$A \approx 989(1.6771)$$
$$A \approx 1658.65$$
* Step 3: Calculate Interest.
$$\text{Interest} = 1658.65 - 989 = 669.65$$
7. At what rate was an investment made that obtains $\$359.80$ in interest compounded annually on $\$668$ over five years?
* Step 1: Identify values. $P = 668$, Interest $= 359.80$, $t = 5$.
* Step 2: Find Total Amount ($A$).
$$A = 668 + 359.80 = 1027.80$$
* Step 3: Solve for $r$.
$$1027.80 = 668(1 + r)^5$$
Divide by $668$:
$$1.5386 = (1 + r)^5$$
Take the 5th root of $1.5386$:
$$1 + r \approx 1.09$$
$$r \approx 0.09$$
Convert to percent: $9\%$
8. How much interest does a $\$182$ investment earn at $10\%$ compounded annually over two years?
* Step 1: Identify values. $P = 182$, $r = 0.10$, $t = 2$.
* Step 2: Find Total Amount ($A$).
$$A = 182(1 + 0.10)^2$$
$$A = 182(1.10)^2$$
$$A = 182(1.21)$$
$$A = 220.22$$
* Step 3: Calculate Interest.
$$\text{Interest} = 220.22 - 182 = 38.22$$
9. You put $\$205$ into an investment at $7\%$ compounded annually for eight years. What will the balance be at the end of eight years?
* Step 1: Identify values. $P = 205$, $r = 0.07$, $t = 8$. "Balance" means Total Amount ($A$).
* Step 2: Plug into the formula.
$$A = 205(1 + 0.07)^8$$
$$A = 205(1.07)^8$$
$$A \approx 205(1.71818)$$
$$A \approx 352.23$$
10. If you invest $\$119$ at an interest rate of $7\%$ compounded annually, how much money will you have after six years?
* Step 1: Identify values. $P = 119$, $r = 0.07$, $t = 6$.
* Step 2: Plug into the formula.
$$A = 119(1 + 0.07)^6$$
$$A = 119(1.07)^6$$
$$A \approx 119(1.50073)$$
$$A \approx 178.59$$
Final Answer:
1. $253.53
2. $804.50
3. $86.33
4. 1.5 years
5. $535.21
6. $669.65
7. 9%
8. $38.22
9. $352.23
10. $178.59
The formula used for all these problems is:
$$A = P(1 + r)^t$$
* $A$ = The final amount (Total money)
* $P$ = The principal (Starting money)
* $r$ = The interest rate (written as a decimal, e.g., $8\% = 0.08$)
* $t$ = Time in years
***
1. How much interest is earned on a principal of $\$432$ invested at an interest rate of $8\%$ compounded annually for six years?
* Step 1: Identify the values. $P = 432$, $r = 0.08$, $t = 6$.
* Step 2: Plug into the formula to find the Total Amount ($A$).
$$A = 432(1 + 0.08)^6$$
$$A = 432(1.08)^6$$
$$A \approx 432(1.58687)$$
$$A \approx 685.53$$
* Step 3: Calculate the Interest. The question asks for *interest*, not the total.
$$\text{Interest} = \text{Total Amount} - \text{Principal}$$
$$\text{Interest} = 685.53 - 432 = 253.53$$
2. If you borrow $\$501$ at $7\%$ compounded annually for seven years, how much will you pay back by the end of the term?
* Step 1: Identify values. $P = 501$, $r = 0.07$, $t = 7$. "Pay back" means the Total Amount ($A$).
* Step 2: Plug into the formula.
$$A = 501(1 + 0.07)^7$$
$$A = 501(1.07)^7$$
$$A \approx 501(1.60578)$$
$$A \approx 804.50$$
3. How much interest is earned on a principal of $\$542$ invested at an interest rate of $3\%$ compounded annually for five years?
* Step 1: Identify values. $P = 542$, $r = 0.03$, $t = 5$.
* Step 2: Find Total Amount ($A$).
$$A = 542(1 + 0.03)^5$$
$$A = 542(1.03)^5$$
$$A \approx 542(1.15927)$$
$$A \approx 628.33$$
* Step 3: Calculate Interest.
$$\text{Interest} = 628.33 - 542 = 86.33$$
4. You put $\$420$ into a savings account with an interest rate of $8\%$ compounded annually which earns $\$53.80$ over a period of time. How long was the period of time?
* Step 1: Identify values. $P = 420$, $r = 0.08$, Interest $= 53.80$.
* Step 2: Find Total Amount ($A$) first.
$$A = 420 + 53.80 = 473.80$$
* Step 3: Set up the equation and solve for $t$.
$$473.80 = 420(1.08)^t$$
Divide both sides by $420$:
$$1.1281 = (1.08)^t$$
Using logarithms or trial and error:
$1.08^1 = 1.08$
$1.08^2 = 1.166$ (Too high)
Let's check closer to 1.5 years? No, usually these are whole numbers. Let's re-calculate precisely.
$\ln(1.1281) / \ln(1.08) \approx 1.5$ years.
*(Note: In many school contexts, if the answer isn't a whole number, it might be rounded. $1.5$ years is the precise mathematical answer).*
5. If you put $\$345$ in a savings account that pays $5\%$ compounded annually for nine years what is the amount of money you will have at the end of the nine years?
* Step 1: Identify values. $P = 345$, $r = 0.05$, $t = 9$.
* Step 2: Plug into the formula.
$$A = 345(1 + 0.05)^9$$
$$A = 345(1.05)^9$$
$$A \approx 345(1.55133)$$
$$A \approx 535.21$$
6. If you put $\$989$ into a savings account that earns $9\%$ compounded annually, how much interest will you receive at the end of six years?
* Step 1: Identify values. $P = 989$, $r = 0.09$, $t = 6$.
* Step 2: Find Total Amount ($A$).
$$A = 989(1 + 0.09)^6$$
$$A = 989(1.09)^6$$
$$A \approx 989(1.6771)$$
$$A \approx 1658.65$$
* Step 3: Calculate Interest.
$$\text{Interest} = 1658.65 - 989 = 669.65$$
7. At what rate was an investment made that obtains $\$359.80$ in interest compounded annually on $\$668$ over five years?
* Step 1: Identify values. $P = 668$, Interest $= 359.80$, $t = 5$.
* Step 2: Find Total Amount ($A$).
$$A = 668 + 359.80 = 1027.80$$
* Step 3: Solve for $r$.
$$1027.80 = 668(1 + r)^5$$
Divide by $668$:
$$1.5386 = (1 + r)^5$$
Take the 5th root of $1.5386$:
$$1 + r \approx 1.09$$
$$r \approx 0.09$$
Convert to percent: $9\%$
8. How much interest does a $\$182$ investment earn at $10\%$ compounded annually over two years?
* Step 1: Identify values. $P = 182$, $r = 0.10$, $t = 2$.
* Step 2: Find Total Amount ($A$).
$$A = 182(1 + 0.10)^2$$
$$A = 182(1.10)^2$$
$$A = 182(1.21)$$
$$A = 220.22$$
* Step 3: Calculate Interest.
$$\text{Interest} = 220.22 - 182 = 38.22$$
9. You put $\$205$ into an investment at $7\%$ compounded annually for eight years. What will the balance be at the end of eight years?
* Step 1: Identify values. $P = 205$, $r = 0.07$, $t = 8$. "Balance" means Total Amount ($A$).
* Step 2: Plug into the formula.
$$A = 205(1 + 0.07)^8$$
$$A = 205(1.07)^8$$
$$A \approx 205(1.71818)$$
$$A \approx 352.23$$
10. If you invest $\$119$ at an interest rate of $7\%$ compounded annually, how much money will you have after six years?
* Step 1: Identify values. $P = 119$, $r = 0.07$, $t = 6$.
* Step 2: Plug into the formula.
$$A = 119(1 + 0.07)^6$$
$$A = 119(1.07)^6$$
$$A \approx 119(1.50073)$$
$$A \approx 178.59$$
Final Answer:
1. $253.53
2. $804.50
3. $86.33
4. 1.5 years
5. $535.21
6. $669.65
7. 9%
8. $38.22
9. $352.23
10. $178.59
Parent Tip: Review the logic above to help your child master the concept of compound interest math worksheet.
