A couple paid back $10,000 for an $8,500 loan. What was the maturity value of the loan?

1. Break Down the Problem

We need to determine the maturity value of a loan. The maturity value is the total amount that must be paid back at the end of the loan term, which includes the principal amount and any interest accrued over the term of the loan.

2. Relevant Concepts

The formula for maturity value (MV) of a loan is given by:

$MV = P + I$

Where:

• $MV$ = Maturity Value
• $P$ = Principal amount (the initial loan amount)
• $I$ = Interest earned on the loan

Given:

• $P = 8,500$
• Total payment made = 10,000

We can find the interest $I$ as follows:

$I = \text{Total Payment} - P$

3. Analysis and Detail

Now, let's calculate the interest:

$I = 10,000 - 8,500 = 1,500$

Thus, the maturity value (MV) of the loan will be the total payment made, which is $10,000$.

4. Verify and Summarize

We calculated the interest to be $1,500$ and added it to the principal of $8,500$. The total payment the couple made is $10,000$, which confirms the maturity value of the loan.

Final Answer

The maturity value of the loan is $10,000.