Compound Interest Worksheet Solutions
The formula for compound interest is given by:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where:
- \( A \) is the amount of money accumulated after \( n \) years, including interest.
- \( P \) is the principal amount (the initial sum of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested or borrowed for, in years.
Since the interest is compounded annually in all the problems, \( n = 1 \). Thus, the formula simplifies to:
\[
A = P (1 + r)^t
\]
####
Problem 1:
Find the amount and the compound interest on \$2500 for 2 years at 10% per annum, compounded annually.
- Principal (\( P \)): \$2500
- Rate (\( r \)): 10% = 0.10
- Time (\( t \)): 2 years
Using the formula:
\[
A = P (1 + r)^t = 2500 \left(1 + 0.10\right)^2 = 2500 \left(1.10\right)^2
\]
Calculate \( (1.10)^2 \):
\[
(1.10)^2 = 1.21
\]
Now, calculate \( A \):
\[
A = 2500 \times 1.21 = 3025
\]
The amount after 2 years is \$3025.
To find the compound interest (\( CI \)):
\[
CI = A - P = 3025 - 2500 = 525
\]
Answer:
\[
\boxed{3025 \text{ (Amount)}, 525 \text{ (Compound Interest)}}
\]
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####
Problem 2:
Find the amount and the compound interest on \$16000 for 3 years at 5% per annum, compounded annually.
- Principal (\( P \)): \$16000
- Rate (\( r \)): 5% = 0.05
- Time (\( t \)): 3 years
Using the formula:
\[
A = P (1 + r)^t = 16000 \left(1 + 0.05\right)^3 = 16000 \left(1.05\right)^3
\]
Calculate \( (1.05)^3 \):
\[
(1.05)^3 = 1.157625
\]
Now, calculate \( A \):
\[
A = 16000 \times 1.157625 = 18522
\]
The amount after 3 years is \$18522.
To find the compound interest (\( CI \)):
\[
CI = A - P = 18522 - 16000 = 2522
\]
Answer:
\[
\boxed{18522 \text{ (Amount)}, 2522 \text{ (Compound Interest)}}
\]
---
####
Problem 3:
Roby obtained a loan of \$25000 from the Syndicate Bank to renovate her house. If the rate of interest is 8% per annum, what amount will she have to pay to the bank after 2 years to discharge her debt?
- Principal (\( P \)): \$25000
- Rate (\( r \)): 8% = 0.08
- Time (\( t \)): 2 years
Using the formula:
\[
A = P (1 + r)^t = 25000 \left(1 + 0.08\right)^2 = 25000 \left(1.08\right)^2
\]
Calculate \( (1.08)^2 \):
\[
(1.08)^2 = 1.1664
\]
Now, calculate \( A \):
\[
A = 25000 \times 1.1664 = 29160
\]
The amount Roby will have to pay after 2 years is \$29160.
Answer:
\[
\boxed{29160}
\]
---
####
Problem 4:
Mike deposited a sum of \$64000 in a post office for 4 years, compounded annually at 4% per annum. What amount will he get on maturity?
- Principal (\( P \)): \$64000
- Rate (\( r \)): 4% = 0.04
- Time (\( t \)): 4 years
Using the formula:
\[
A = P (1 + r)^t = 64000 \left(1 + 0.04\right)^4 = 64000 \left(1.04\right)^4
\]
Calculate \( (1.04)^4 \):
\[
(1.04)^4 = 1.16985856
\]
Now, calculate \( A \):
\[
A = 64000 \times 1.16985856 = 74870.4
\]
The amount Mike will get on maturity is \$74870.40.
Answer:
\[
\boxed{74870.40}
\]
---
Final Answers:
1. \(\boxed{3025 \text{ (Amount)}, 525 \text{ (Compound Interest)}}\)
2. \(\boxed{18522 \text{ (Amount)}, 2522 \text{ (Compound Interest)}}\)
3. \(\boxed{29160}\)
4. \(\boxed{74870.40}\)
Parent Tip: Review the logic above to help your child master the concept of compound interest word problems worksheets.
