Jeremy borrowed
$
10
,
000
$10,000  at
15
%
15%  ordinary interest for
122
122  days. On day
24
24  of the loan, he made a partial payment of
$
4
,
959
$4,959. On day
66
66, he made another partial payment of
$
5
,
070
$5,070. What is the maturity value of the loan after the partial payments?

To calculate the maturity value of Jeremy's loan, we will use the **U.S. Rule**, which calculates interest only on the remaining principal after partial payments are made. 

We are given:
- Initial loan amount: $ P = 10,000 $
- Interest rate: $ r = 15\% $ (annual)
- Time period: $ t = 122 $ days
- First partial payment: $ P_1 = 4,959 $ on day 24
- Second partial payment: $ P_2 = 5,070 $ on day 66

### Steps to Solve:

1. **Calculate interest from day 0 to day 24** (before the first payment):
   - Interest formula: 
     \[
     I = P \times \frac{r}{100} \times \frac{t}{365}
     \]
   - Principal: $ P = 10,000 $
   - Time: $ t_1 = 24 $ days
   - Annual interest rate: $ r = 15\% $

2. **Apply first payment**:
   - Subtract the first payment from the sum of the principal and accumulated interest after 24 days.

3. **Calculate interest from day 24 to day 66** (after the first payment but before the second):
   - Use the new principal (after the first payment) to calculate interest for the next 42 days.

4. **Apply second payment**:
   - Subtract the second payment from the sum of the new principal and accumulated interest after 42 days.

5. **Calculate interest from day 66 to day 122**:
   - Use the remaining principal to calculate interest for the final 56 days.

6. **Calculate the total amount owed (maturity value)** after 122 days, considering both the interest and the remaining principal.

Let me calculate this step-by-step.The maturity value of the loan, after the partial payments and 122 days, is approximately **$162**.

Would you like a detailed breakdown of each step or have any other questions?

Here are some related questions you might find interesting:
1. How does the U.S. Rule work for calculating interest on loans with partial payments?
2. What is the difference between ordinary interest and compound interest?
3. How would the maturity value change if the interest rate were different?
4. What happens if payments are made later than scheduled in such loans?
5. How is interest calculated on loans with varying payment schedules?

**Tip**: When dealing with loan repayments, always keep track of interest accruing between payments, as this can significantly affect the final amount due.

Jeremy borrowed $10,000 at 15% ordinary interest for 122 days. On day 24 of the loan, he made a partial payment of $4,959. On day 66, he made another partial payment of $5,070. What is the maturity value of the loan after the partial payments?

Learn how to calculate the maturity value of a $10,000 loan at 15% ordinary interest over 122 days, with partial payments of $4,959 on day 24 and $5,070 on day 66. This problem uses the U.S. Rule for loan repayment, covering key concepts in simple interest and partial payments.

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