Jeremy borrowed  
$
36
,
000
$36,000  at  
14
%
14%  ordinary interest for  
107
107  days. On day  
27
27  of the loan, he made a partial payment of  
$
3
,
767
$3,767. On day  
67
67, he made another partial payment of  
$
5
,
768
$5,768. What is the maturity value of the loan after the partial payments?

To solve this, we need to calculate the maturity value of Jeremy's loan after the partial payments. This problem involves using the concept of **ordinary interest** and **partial payments**.

### Step 1: Calculate the initial interest for the full loan before any payments are made.

- Principal: $ P = 36,000 $
- Interest rate: $ r = 14\% $ annually
- Time: $ t = 107 \, \text{days} $

Using **ordinary interest**, the formula is:

\[
I = P \times r \times \frac{t}{360}
\]

Substitute the values:

\[
I = 36,000 \times 0.14 \times \frac{107}{360}
\]

\[
I = 36,000 \times 0.14 \times 0.2972 \approx 1,498.22
\]

Thus, the total interest for the full term (107 days) is approximately **$1,498.22**.

### Step 2: Calculate the balance after the first partial payment on day 27.

First, calculate the interest accrued from day 1 to day 27:

\[
I_1 = 36,000 \times 0.14 \times \frac{27}{360} = 36,000 \times 0.14 \times 0.075 = 378
\]

The interest accrued by day 27 is **$378**.

Now, after Jeremy makes a payment of **$3,767**, the remaining balance is:

\[
\text{New Principal} = 36,000 + 378 - 3,767 = 32,611
\]

### Step 3: Calculate the balance after the second partial payment on day 67.

Now, calculate the interest accrued from day 27 to day 67 (40 days) on the new principal of $32,611:

\[
I_2 = 32,611 \times 0.14 \times \frac{40}{360} = 32,611 \times 0.14 \times 0.1111 \approx 508.51
\]

The interest accrued by day 67 is approximately **$508.51**.

After Jeremy makes the second payment of **$5,768**, the new balance becomes:

\[
\text{New Principal} = 32,611 + 508.51 - 5,768 = 27,351.51
\]

### Step 4: Calculate the interest for the remaining days (day 67 to day 107).

Now, calculate the interest accrued from day 67 to day 107 (40 days) on the new principal of $27,351.51:

\[
I_3 = 27,351.51 \times 0.14 \times \frac{40}{360} = 27,351.51 \times 0.14 \times 0.1111 \approx 426.23
\]

The interest accrued for the remaining 40 days is approximately **$426.23**.

### Step 5: Calculate the maturity value.

The maturity value is the sum of the remaining balance after day 67 plus the interest accrued from day 67 to day 107:

\[
\text{Maturity Value} = 27,351.51 + 426.23 = 27,777.74
\]

Thus, the maturity value of the loan after the partial payments is **$27,777.74**.

---

Would you like a breakdown of any particular step or further details? Here are some related questions to help you explore:

1. How is ordinary interest different from compound interest?
2. What if Jeremy made no partial payments—what would the maturity value be then?
3. How would the calculation change if the loan were compounded monthly?
4. Can you explain the concept of the time factor in ordinary interest calculations?
5. What happens if the interest rate changes midway through the loan period?

**Tip**: Always keep track of the time intervals between partial payments to apply the correct interest.

Jeremy borrowed $36,000 at 14% ordinary interest for 107 days. On day 27 of the loan, he made a partial payment of $3,767. On day 67, he made another partial payment of $5,768. What is the maturity value of the loan after the partial payments?

Learn how to calculate the maturity value of a $36,000 loan with 14% ordinary interest over 107 days after two partial payments. This detailed solution breaks down the interest and balance calculations step by step, suitable for finance students and advanced math learners.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation