A partial payment is made on the date indicated. Find the balance due on the note on the date of maturity:
Principal: $108,000 Maturity date: November 1
Rate: 14% Partial payment. $27,000 on August 15
Effective date: February 15th
To find the balance due on the note on the date of maturity, we need to follow these steps:
Step 1: Calculate the time between the effective date and the maturity date.
- The effective date is February 15th.
- The maturity date is November 1st.
- The time between the effective date and the maturity date is 8 months and 17 days.
Step 2: Calculate the interest accrued from the effective date to the partial payment date.
- The effective date is February 15th.
- The partial payment date is August 15th.
- The time between the effective date and the partial payment date is 6 months.
Step 3: Calculate the interest accrued on the partial payment.
- The partial payment amount is $27,000.
- The interest rate is 14% per annum.
- The interest accrued on the partial payment is calculated by multiplying the partial payment amount by the interest rate and the time between the effective date and the partial payment date (in years).
- The interest accrued on the partial payment is $27,000 * 14% * (6/12) = $1,890.
Step 4: Calculate the interest accrued from the partial payment date to the maturity date.
- The partial payment date is August 15th.
- The maturity date is November 1st.
- The time between the partial payment date and the maturity date is 2 months and 17 days.
Step 5: Calculate the interest accrued on the remaining principal.
- The remaining principal is $108,000 - $27,000 = $81,000.
- The interest rate is 14% per annum.
- The interest accrued on the remaining principal is calculated by multiplying the remaining principal by the interest rate and the time between the partial payment date and the maturity date (in years).
- The interest accrued on the remaining principal is $81,000 * 14% * (2/12) = $1,890.
Step 6: Calculate the total interest accrued.
- The total interest accrued is the sum of the interest accrued on the partial payment and the interest accrued on the remaining principal.
- The total interest accrued is $1,890 + $1,890 = $3,780.
Step 7: Calculate the balance due on the note on the date of maturity.
- The balance due on the note on the date of maturity is the sum of the remaining principal and the total interest accrued.
- The balance due on the note on the date of maturity is $81,000 + $3,780 = $84,780.
Therefore, the balance due on the note on the date of maturity is $84,780.