Mortgage Interest Calculation for First National Bank's Loans A and B
Question
Mrs. Franklin has two mortgage loans at First National Bank on which she makes monthly payments. On Loan A she made 13 payments last year, mailing the last payment on December 28. It was received the afternoon of January 2 and credited on January 3. The amount of interest paid on Loan A in the first 12 payments was $1,000. There was $155 of interest on the 13th payment. On Loan B, she made 12 payments; each contained interest accrued to the fourth day of the month.
The last payment was mailed on December 19 and was received and credited on December 23. The last payment contained interest accrued to January 4. The total interest paid on Loan B was $2,000, of which $100 accrued between January 1 and January 4 of the next year. How much interest must First National Bank report?
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A. B. C. D.C
This question is testing your ability to calculate interest payments on loans based on specific payment schedules and dates.
Let's start with Loan A:
Mrs. Franklin made 13 payments on Loan A last year, and the last payment was mailed on December 28 but received and credited on January 3 of the following year. This means that the last payment was not made within the calendar year, so we need to separate out the interest paid in the calendar year from the interest paid in the following year.
The amount of interest paid on Loan A in the first 12 payments was $1,000, which means that each of these payments included $83.33 of interest ($1,000 divided by 12 payments). The 13th payment included $155 of interest.
To calculate the interest paid in the calendar year, we need to subtract the interest paid on the 13th payment from the total interest paid on Loan A in the year. This gives us:
$1,000 + $155 - $83.33 = $1,071.67
So the interest that First National Bank must report for Loan A is $1,071.67.
Now let's move on to Loan B:
Mrs. Franklin made 12 payments on Loan B, and the last payment was mailed on December 19 but received and credited on December 23 of the same year. The last payment included interest accrued to January 4 of the following year, so we need to separate out the interest paid in the calendar year from the interest paid in the following year.
We know that the total interest paid on Loan B was $2,000, of which $100 accrued between January 1 and January 4 of the following year. This means that the interest paid in the calendar year was:
$2,000 - $100 = $1,900
Each of the 12 payments on Loan B contained interest accrued to the fourth day of the month. This means that each payment covered interest for the first three days of the month, plus the remaining days of the month. To calculate the total interest accrued in the calendar year, we need to calculate the interest accrued for the first three days of each month, and add it to the interest accrued for the remaining days of the month.
Assuming a 30-day month, the interest accrued for the first three days of each month is:
Loan balance x interest rate x 3/30
Since we don't have information about the loan balance or interest rate, we can't calculate this directly. However, we know that the total interest accrued in the calendar year was $1,900, so we can use this information to solve for the interest rate.
Assuming that the loan balance was constant over the year, the average balance would be:
($1 x 1 + $2 x 11)/12 = $1.91
This means that the interest rate can be calculated as:
$1,900/($1.91 x 12 x 3/30) = 0.4161 or 41.61%
Using this interest rate, we can calculate the interest accrued for the remaining days of each month as:
Loan balance x interest rate x (30 - 3)/30
Assuming a constant loan balance of $100,000, this gives us:
$100,000 x 0.4161 x 27/30 x 12 = $11,909.56
So the total interest paid on Loan B in the calendar year was:
$11,909.56 + $100 = $12,009.56
Therefore, the interest that First National Bank must report for Loan B is $12,009.56.
Adding the interest for Loan A and Loan B together, we get:
$1,
