this table can be used to organize rajs credit card balances and payments over 6 months. the annual…

Explanation:

Step1: Calculate Interest for Month 2

The formula for interest charged is ( \text{Interest} = \text{Balance} \times \text{Interest Rate} ). For month 2, balance is $406 and rate is 0.015. ( 406 \times 0.015 = 6.09 )

Step2: Calculate Interest for Month 3

Balance is $361.34, rate 0.015. ( 361.34 \times 0.015 = 5.4201 \approx 5.42 )

Step3: Calculate Interest for Month 4

Balance is $316.01, rate 0.015. ( 316.01 \times 0.015 = 4.74015 \approx 4.74 )

Step4: Calculate Interest for Month 5

Balance is $270, rate 0.015. ( 270 \times 0.015 = 4.05 )

Step5: Calculate Interest for Month 6

Balance is $223.30, rate 0.015. ( 223.30 \times 0.015 = 3.3495 \approx 3.35 )

Step6: Sum All Interests

Month 1: $6.00, Month 2: $6.09, Month 3: $5.42, Month 4: $4.74, Month 5: $4.05, Month 6: $3.35. Total = ( 6.00 + 6.09 + 5.42 + 4.74 + 4.05 + 3.35 ) First, ( 6.00 + 6.09 = 12.09 ) Then, ( 12.09 + 5.42 = 17.51 ) Then, ( 17.51 + 4.74 = 22.25 ) Then, ( 22.25 + 4.05 = 26.30 ) Then, ( 26.30 + 3.35 = 29.65 ) Wait, let's recalculate with more precise values (without rounding intermediate steps):

Month 2: ( 406 \times 0.015 = 6.09 )

Month 3: ( 361.34 \times 0.015 = 5.4201 )

Month 4: ( 316.01 \times 0.015 = 4.74015 )

Month 5: ( 270 \times 0.015 = 4.05 )

Month 6: ( 223.30 \times 0.015 = 3.3495 )

Now sum: ( 6.00 + 6.09 + 5.4201 + 4.74015 + 4.05 + 3.3495 )

( 6.00 + 6.09 = 12.09 )

( 12.09 + 5.4201 = 17.5101 )

( 17.5101 + 4.74015 = 22.25025 )

( 22.25025 + 4.05 = 26.30025 )

( 26.30025 + 3.3495 = 29.64975 \approx 29.65 ) (or more precisely, let's check if we made a mistake in month 3 balance. Wait, the table for month 3: balance is $361.34? Wait, let's re - check the balance calculation. Wait, maybe the balance for month 3 is calculated as (Month 2 balance - payment)+interest? Wait, no, the problem is to calculate interest charged each month as balance * rate. Wait, maybe my initial balance for month 3 is wrong? Wait, month 2 balance is $406, payment is $50, so new balance should be ( 406 - 50 + (406 \times 0.015)= 356 + 6.09 = 362.09 )? Wait, the table says month 3 balance is $361.34. Oh, maybe the table has already accounted for interest. So we should use the balance given in the table for each month to calculate interest. So month 3 balance is $361.34, so interest is ( 361.34 \times 0.015 = 5.4201 ), month 4 balance is $316.01, so interest is ( 316.01 \times 0.015 = 4.74015 ), month 5 balance is $270, interest ( 270 \times 0.015 = 4.05 ), month 6 balance is $223.30, interest ( 223.30 \times 0.015 = 3.3495 ).

Now sum all interests:

Month 1: 6.00

Month 2: 406 * 0.015 = 6.09

Month 3: 361.34 * 0.015 = 5.4201

Month 4: 316.01 * 0.015 = 4.74015

Month 5: 270 * 0.015 = 4.05

Month 6: 223.30 * 0.015 = 3.3495

Now add them up:

6.00 + 6.09 = 12.09

12.09 + 5.4201 = 17.5101

17.5101 + 4.74015 = 22.25025

22.25025 + 4.05 = 26.30025

26.30025 + 3.3495 = 29.64975 ≈ 29.65

Wait, but let's check again. Maybe the table's month 3 balance is calculated as (month 2 balance - payment) + month 2 interest? Month 2 balance: $406, payment: $50, so 406 - 50 = 356, plus month 2 interest $6.09? No, 356 + 6.09 = 362.09, but the table says $361.34. So maybe there's a rounding in the table. But according to the table, we use the given balance to calculate interest. So proceeding with the table's balances:

So total interest is 6.00 (month1) + (4060.015) (month2) + (361.340.015) (month3) + (316.010.015) (month4) + (2700.015) (month5) + (223.30*0.015) (month6)

Calculating each:

Month1: 6.00

Month2: 406*0.015 = 6.09

Month3: 361.34*0.015 = 5.4201

Month4: 316.01*0.015 = 4.74015

Month5: 270*0.015 = 4.05

Month6: 223.30*0.015 = 3.3495

Now sum: 6.00 + 6.09 = 12.09; 12.09 + 5.4201 = 17.5101; 17.5101 + 4.74015 = 22.25025; 22.25025 + 4.05 = 26.30025; 26.30025 + 3.3495 = 29.64975, which is approximately $29.65.

But let's check with another approach. Maybe the interest is calculated as (previous balance - payment) * rate? No, the formula for credit card interest is usually average daily balance, but here the table gives the balance, so we use balance * monthly rate (0.015 is 18%/12).

Alternatively, maybe the table's month 3 balance is 406 - 50 + 6.09 = 362.09, but it's given as 361.34, so there's a rounding difference. But according to the problem, we use the table's balances to calculate interest. So the total interest is the sum of each month's interest charged, where interest charged = balance * 0.015.

So:

Month 1: 500 * 0.015 = 7.5? Wait, wait a minute! Oh no! I made a mistake here. The first month: balance is $500, interest rate 0.015, so interest charged should be 500 * 0.015 = $7.50, but the table says $6.00. Wait, that's a problem. Wait, the table says month 1: balance $500, payment $100, interest rate 0.015, interest charged $6.00. Wait, 500 * 0.015 is 7.5, but the table says $6.00. So maybe the interest is calculated on (balance - payment)? No, 500 - 100 = 400, 400 * 0.015 = 6.00. Ah! So the interest is charged on the balance after payment? Wait, that's a different formula. So maybe the formula is Interest = (Balance - Payment) * Interest Rate? Wait, month 1: balance $500, payment $100, so 500 - 100 = 400, 400 * 0.015 = 6.00, which matches the table. Oh! I made a mistake in the formula. So the correct formula is Interest = (Balance - Payment) * Interest Rate? Wait, month 2: balance $406, payment $50, so 406 - 50 = 356, 356 * 0.015 = 5.34, but the table doesn't have month 2 interest. Wait, no, the table's month 1: balance $500, payment $100, interest charged $6.00, which is (500 - 100)0.015 = 4000.015=6.00. Then month 2: balance $406, payment $50, so (406 - 50)0.015 = 3560.015=5.34? But the table doesn't show month 2 interest. Wait, the table has month 1: interest charged $6.00, month 2: no interest charged shown, month 3: no, etc. Wait, the table is organized as:

Month | Balance | Payment | Interest Rate | Interest Charged

1 | 500 | 100 | 0.015 | 6.00

2 | 406 | 50 | 0.015 |?

3 | 361.34 | 50 | 0.015 |?

4 | 316.01 | 50 | 0.015 |?

5 | 270 | 50 | 0.015 |?

6 | 223.30 | 50 | 0.015 |?

Then the next row: 6 | 223.30 | 50 | 0.015 |?

Wait, the user's table:

Month 1: Balance $500, Payment $100, Interest Rate 0.015, Interest Charged $6.00

Month 2: Balance $406, Payment $50, Interest Rate 0.015, Interest Charged (empty)

Month 3: Balance $361.34, Payment $50, Interest Rate 0.015, Interest Charged (empty)

Month 4: Balance $316.01, Payment $50, Interest Rate 0.015, Interest Charged (empty)

Month 5: Balance $270, Payment $50, Interest Rate 0.015, Interest Charged (empty)

Month 6: Balance $223.30, Payment $50, Interest Rate 0.015, Interest Charged (empty)

Then the last row: 6 | 223.30 | 50 | 0.015 |?

Wait, no, the table is:

Row 1: Month 1, Balance 500, Payment 100, Rate 0.015, Interest 6.00

Row 2: Month 2, Balance 406, Payment 50, Rate 0.015, Interest (empty)

Row 3: Month 3, Balance 361.34, Payment 50, Rate 0.015, Interest (empty)

Row 4: Month 4, Balance 316.01, Payment 50, Rate 0.015, Interest (empty)

Row 5: Month 5, Balance 270, Payment 50, Rate 0.015, Interest (empty)

Row 6: Month 6, Balance 223.30, Payment 50, Rate 0.015, Interest (empty)

Then the last row (maybe month 7? But the question is first 6 months). Wait, the question is "What is the amount of total interest charged for the first 6 months?"

But in month 1, interest is $6.00, which is (500 - 100)0.015 = 4000.015=6.00.

Month 2: balance is $406, payment $50, so (406 - 50)=356, 356*0.015=5.34? But the balance for month 3 is $361.34. 356 + 5.34=361.34. Ah! So the balance for month n+1 is (balance_n - payment_n) + interest_n. So interest_n = (balance_n - payment_n) * interest rate.

So let's recalculate:

Month 1:

Balance: $500, Payment: $100, so (500 - 100)=400, Interest: 400*0.015=6.00 (matches table)

Month 2:

Balance: $406 (which is (500 - 100) + 6.00 = 406), Payment: $50, so (406 - 50)=356, Interest: 356*0.015=5.34

Month 3:

Balance: $361.34 (which is 356 + 5.34=361.34), Payment: $50, so (361.34 - 50)=311.34, Interest: 311.34*0.015=4.6701

Month 4:

Balance: $316.01 (311.34 + 4.6701=316.0101≈316.01), Payment: $50, so (316.01 - 50)=266.01, Interest: 266.01*0.015=3.99015

Month 5:

Balance: $270 (266.01 + 3.99015=300.00015? No, table says $270. Wait, maybe my approach is wrong. Alternatively, the interest is charged on the balance before payment. But month 1: 500*0.015=7.5, but table says 6.00. So there's a discrepancy. But the table gives month 1 interest as $6.00, so we have to go with