To determine the new maturity value of the loan after the partial payment, we need to calculate the interest on the remaining balance for the remaining period.
Here are the steps to calculate the new maturity value:
1. Calculate the interest accrued until the partial payment:
- Determine the daily interest rate: Divide the annual interest rate by 365 days. In this case, 12% divided by 365 gives us a daily interest rate of approximately 0.0329%.
- Calculate the interest accrued until day 20: Multiply the daily interest rate by the principal amount ($50,000) and the number of days (20). This gives us an interest of approximately $328.33.
2. Determine the remaining balance after the partial payment:
- Subtract the partial payment amount ($5,000) from the original principal amount ($50,000). The remaining balance is $45,000.
3. Calculate the interest on the remaining balance for the remaining period:
- Determine the number of days remaining in the loan term: Subtract day 20 from the total loan period of 60 days. This gives us 40 remaining days.
- Calculate the interest on the remaining balance: Multiply the remaining balance ($45,000) by the daily interest rate (0.0329%) and the number of remaining days (40). This gives us an interest of approximately $471.60.
4. Determine the new maturity value:
- Add the interest accrued until the partial payment ($328.33) to the interest on the remaining balance ($471.60). This gives us a total interest of approximately $799.93.
- Add the total interest to the remaining balance ($45,000) to find the new maturity value. The new maturity value of the loan is approximately $45,799.93.
In summary, the new maturity value of the loan after the partial payment is approximately $45,799.93.