Solve Amortization Contradiction: 5yr $20k Loan @ 10% Compounded Annually

  • Thread starter IniquiTrance
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In summary, amortization is the process of paying off a debt over time by making regular payments that cover both the principal amount borrowed and the interest accrued. This includes loans such as a 5-year $20,000 loan with a 10% annual interest rate, where interest is compounded annually. When solving amortization, a contradiction can arise if there are discrepancies between expected and actual payment schedules. This can be resolved by carefully reviewing calculations and seeking professional help if needed. Failure to resolve an amortization contradiction can result in owing more than expected or damaging credit score.
  • #1
IniquiTrance
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Say I have a 5 year $20,000 mortgage at 10% compounded annually.

To calculate the annual payment:

[tex]\frac{x}{(1.10)} + \frac{x}{(1.10)^{2}} + \frac{x}{(1.10)^{3}} + + \frac{x}{(1.10)^{4}} + \frac{x}{(1.10)^{5}} = 20,000 [/tex]

The first term corresponds to the first year and so on.

It would seem then that this 1st term knocks off the largest chunk of the 20k principal, since it has the largest value. Yet I know that the largest principal payment is made in the last year, when interest is lowest.

How do I resolve this contradiction?

Thanks
 
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  • #2
Most of the first chunk goes toward interest. At least, that's how it's usually explained.
 

1. What is amortization?

Amortization is the process of paying off a debt over time by making regular payments that cover both the principal amount borrowed and the interest accrued.

2. What is a 5yr $20k loan @ 10% compounded annually?

This refers to a loan in which the borrower receives $20,000 and agrees to pay it back over a period of 5 years with an annual interest rate of 10%. The interest is calculated and added to the principal amount each year, resulting in a higher total amount owed.

3. What is the contradiction in solving amortization?

The contradiction in solving amortization arises when there is a mismatch between the expected payment schedule and the actual payment schedule. This can happen when there are errors in the calculation of interest or when payments are missed or made late.

4. How can I solve the amortization contradiction?

The best way to solve the amortization contradiction is to carefully review all calculations and payment schedules, and identify any discrepancies or errors. If necessary, consult with a financial professional for assistance in resolving the contradiction.

5. What are the consequences of not resolving an amortization contradiction?

If an amortization contradiction is not resolved, it can result in the borrower owing more than they expected or being unable to pay off the loan in the agreed upon timeframe. This can lead to financial strain and potentially damage the borrower's credit score.

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