Question

Max Wholesaler borrowed $5,500 on a 10%, 120-day note, After 45 days, Max paid $1,925 on the note. Thirty days later, Max paid an additional $1,650. Use ordinary interest. a. Determine the total interest using the U.S. Rule. Note: Round your intermediate balances and interest amounts to the nearest cent. Round your final answer to the nearest cent. b. Determine the ending balance due using the U.S. Rule. Note: Round your intermediate balances and interest amounts to the nearest cent. Round your final answer to the nearest cent.

Answer 1

a. The total interest using the U.S. Rule is approximately $783.70.

b. The ending balance due using the U.S. Rule is approximately $2708.70.

To calculate the total interest and the ending balance due using the U.S. Rule, which is based on ordinary interest, we'll break down the payments and compute the interest at each step.

Given data:

- Principal amount (P) = $5,500

- Interest rate = 10%

- Time = 120 days

- Payment 1 after 45 days = $1,925

- Payment 2 after 75 days (45 + 30 days) = $1,650

Calculation:

First, let's calculate the interest for the initial 45 days:

`\[ I = P * r * t \]`

`\[ I = 5500 * 0.10 * (45)/(365) \]`

`\[ I \approx 673.97 \]`

So, after 45 days, the interest accrued is approximately $673.97.

Max paid $1,925 after 45 days. The excess amount over the accrued interest will be applied to reduce the principal.

`\[ Excess\ Payment = Payment\ -\ Interest\ (for\ 45\ days) \]`

`\[ Excess\ Payment = 1925 - 673.97 = 1251.03 \]`

Now, let's calculate the balance after 45 days:

`\[ Balance\ after\ 45\ days = Principal - Excess\ Payment \]`

`\[ Balance\ after\ 45\ days = 5500 - 1251.03 = 4248.97 \]`

Now, we'll calculate the interest for the next 30 days on the remaining balance:

`\[ I = Balance\ after\ 45\ days * 0.10 * (30)/(365) \]`

`\[ I \approx 109.73 \]`

After the second payment of $1,650, the excess payment will be applied to the remaining principal:

`\[ Excess\ Payment\ (2nd\ payment) = 1650 - 109.73 = 1540.27 \]`

Finally, let's calculate the ending balance due after the second payment:

`\[ Ending\ Balance = Balance\ after\ 45\ days - Excess\ Payment\ (2nd\ payment) \]`

`\[ Ending\ Balance = 4248.97 - 1540.27 = 2708.70 \]`

Answer 2

The total interest on the note, using the U.S. Rule, is $122.60.

The ending balance due using the U.S. Rule. is $2,047.60

a. Computation of the total interest using the U.S. Rule:

Initial Principal = $5,500

Interest = Principal × Rate × Time

= $5,500 × 0.10 × (45/360)

= $68.75

Balance after 45 days = Initial Principal - First Payment

= $5,500 - $1,925

= $3,575

Interest = Remaining Balance × Rate × Time

= $3,575 × 0.10 × (30/360)

= $29.79

Balance after 75 days (second payment):

= Previous Balance - Second Payment

= $3,575 - $1,650

= $1,925

The interest on the remaining balance for the last 45 days:

= Remaining Balance × Rate × Time

= $1,925 × 0.10 × (45/360)

= $24.06

Total Interest = Interest from Step 2 + Interest from Step 4 + Interest from Step 6

= $68.75 + $29.79 + $24.06

= $122.60

Therefore, the total interest on the note, using the U.S. Rule, is $122.60.

b. Ending balance = Principal + Total interest

= $1,925 + $122.60

= $2,047.60.