Question

1. $1,020 at 6% for $2\frac{1}{2}$ years
2. $7,800 at 12% for 2 years
3. $34,000 at 8% for $4\frac{1}{2}$ years
4. $52,200 at 4% for $6\frac{3}{4}$ years

Explanation:

Step1: Identify the formula for simple interest

The formula for simple interest is \( I = P \times r \times t \), where \( I \) is the interest, \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal form), and \( t \) is the time in years.

Step2: Solve problem 23

Sub - step 1: Convert the rate and time

For problem 23: \( P=\$1020 \), \( r = 6\%=0.06 \), \( t = 2\frac{1}{2}=\frac{5}{2} = 2.5 \) years.

Sub - step 2: Calculate the interest

Using the formula \( I=P\times r\times t \), we substitute the values:
\( I = 1020\times0.06\times2.5 \)
First, calculate \( 1020\times0.06 = 61.2 \)
Then, \( 61.2\times2.5=153 \)

Step3: Solve problem 25

Sub - step 1: Convert the rate and time

For problem 25: \( P = \$7800 \), \( r=12\% = 0.12 \), \( t = 2 \) years.

Sub - step 2: Calculate the interest

Using the formula \( I = P\times r\times t \)
\( I=7800\times0.12\times2 \)
First, \( 7800\times0.12 = 936 \)
Then, \( 936\times2 = 1872 \)

Step4: Solve problem 27

Sub - step 1: Convert the rate and time

For problem 27: \( P=\$34000 \), \( r = 8\%=0.08 \), \( t=4\frac{1}{2}=\frac{9}{2}=4.5 \) years.

Sub - step 2: Calculate the interest

Using the formula \( I = P\times r\times t \)
\( I=34000\times0.08\times4.5 \)
First, \( 34000\times0.08 = 2720 \)
Then, \( 2720\times4.5=12240 \)

Step5: Solve problem 29

Sub - step 1: Convert the rate and time

For problem 29: \( P = \$52200 \), \( r = 4\%=0.04 \), \( t=6\frac{3}{4}=\frac{27}{4} = 6.75 \) years.

Sub - step 2: Calculate the interest

Using the formula \( I=P\times r\times t \)
\( I = 52200\times0.04\times6.75 \)
First, \( 52200\times0.04=2088 \)
Then, \( 2088\times6.75 = 2088\times(6 + 0.75)=2088\times6+2088\times0.75=12528+1566 = 14094 \)

Answer:

• Problem 23: The simple interest is \(\$153\)
• Problem 25: The simple interest is \(\$1872\)
• Problem 27: The simple interest is \(\$12240\)
• Problem 29: The simple interest is \(\$14094\)