Let's go through each of the problems step by step.
A. Sharif's Savings Account
-
Interest earned after 2 years:
-
Formula for simple interest: \[ I = P \times r \times t \]
-
Where:
- \( P = 2500 \) (principal)
- \( r = 0.05 \) (annual interest rate)
- \( t = 2 \) (time in years)
-
Calculation: \[ I = 2500 \times 0.05 \times 2 = 2500 \times 0.1 = 250 \]
-
So, after 2 years, Sharif will earn $250 in interest.
-
-
Total amount in the account after 12 years:
-
For 12 years:
-
Calculation: \[ I = 2500 \times 0.05 \times 12 = 2500 \times 0.6 = 1500 \]
-
Total amount = Principal + Interest: \[ 2500 + 1500 = 4000 \]
-
So, Sharif will have $4000 in the savings account after 12 years.
-
B. Chang's Account
-
Finding the annual interest rate:
-
Total interest earned over 4 years = $100
-
Using the formula: \[ I = P \times r \times t \]
-
Rearranged to find \( r \): \[ r = \frac{I}{P \times t} \]
-
Where:
- \( I = 100 \)
- \( P = 1000 \)
- \( t = 4 \)
-
Calculation: \[ r = \frac{100}{1000 \times 4} = \frac{100}{4000} = 0.025 \]
-
So, the annual interest rate is 2.5%.
-
-
Amount in the account after 15 years:
-
Using the 2.5% rate:
-
Total interest over 15 years: \[ I = 1000 \times 0.025 \times 15 = 1000 \times 0.375 = 375 \]
-
Total amount: \[ 1000 + 375 = 1375 \]
-
So, Chang will have $1375 in the savings account after 15 years.
-
C. Bank Savings Account
- Finding time to earn $100 in interest with a principal of $800:
-
With a principal of $800, the interest rate is 2%.
-
Using the formula: \[ t = \frac{I}{P \times r} \]
-
Where:
- \( I = 100 \)
- \( P = 800 \)
- \( r = 0.02 \)
-
Calculation: \[ t = \frac{100}{800 \times 0.02} = \frac{100}{16} = 6.25 \]
-
So, it takes 6.25 years to earn $100 in interest.
-
D. Laptop Loan
-
Finding the original amount borrowed:
-
Using the formula for total amount paid back: \[ A = P + I \] \[ I = P \times r \times t \]
-
We know:
-
\( A = 1050 \)
-
\( r = 0.15 \)
-
\( t = 5 \)
-
Rearranging gives: \[ A = P + (P \times 0.15 \times 5) \] \[ 1050 = P + 0.75P \] \[ 1050 = 1.75P \]
-
Solving for \( P \): \[ P = \frac{1050}{1.75} = 600 \]
-
So, the amount borrowed for the laptop is $600.
-
-
Finding the interest paid:
-
Using \( I = P \times r \times t \): \[ I = 600 \times 0.15 \times 5 = 600 \times 0.75 = 450 \]
-
Thus, the interest paid is $450.
-
E. Finding the Annual Interest Rate (R)
- Using the given values:
-
Using the formula \( I = P \times r \times t \):
-
Rearranging gives: \[ r = \frac{I}{P \times t} \]
-
Where:
- \( I = 24 \)
- \( P = 400 \)
- \( t = 2 \)
-
Calculation: \[ r = \frac{24}{400 \times 2} = \frac{24}{800} = 0.03 \]
-
So, the annual interest rate \( R \) is 3%.
-