To determine the total interest charged over the first 6 months, follow these steps:
1. Understand the given data:
- Raj's initial balance and the payments he made each month are given.
- The interest rate charge is 1.5% per month.
2. Calculate the interest for each month:
- Month 1:
- Balance = \$500
- Payment = \$100
- Monthly interest rate = 1.5%
- Interest charged = \( \[tex]$500 \times 0.015 = \$[/tex]7.50 \)
- Month 2:
- New Balance = \[tex]$406 (after payment of \$[/tex]100 from month 1)
- Payment = \$50
- Interest charged = \( \[tex]$406 \times 0.015 = \$[/tex]6.09 \)
- Month 3:
- New Balance = \[tex]$361.34 (after payment of \$[/tex]50 from month 2)
- Payment = \$50
- Interest charged = \( \[tex]$361.34 \times 0.015 = \$[/tex]5.42 \)
- Month 4:
- New Balance = \[tex]$316.01 (after payment of \$[/tex]50 from month 3)
- Payment = \$50
- Interest charged = \( \[tex]$316.01 \times 0.015 = \$[/tex]4.74 \)
- Month 5:
- New Balance = \[tex]$270 (after payment of \$[/tex]50 from month 4)
- Payment = \$50
- Interest charged = \( \[tex]$270 \times 0.015 = \$[/tex]4.05 \)
- Month 6:
- New Balance = \[tex]$223.30 (after payment of \$[/tex]50 from month 5)
- Payment = \$50
- Interest charged = \( \[tex]$223.30 \times 0.015 = \$[/tex]3.35 \)
3. Sum up the interest charged over the 6 months:
- Total interest = \( \[tex]$7.50 + \$[/tex]6.09 + \[tex]$5.42 + \$[/tex]4.74 + \[tex]$4.05 + \$[/tex]3.35 = \$31.15 \)
Thus, the total interest charged for the first 6 months is \$31.14975.
