4. How much interest will you pay in the 16th year of a $100,000, 5.5%, 25 year mortgage,...

Question:

4. How much interest will you pay in the 16th year of a $100,000, 5.5%, 25 year mortgage, assuming annual compounding?

Mortgage Amortization:

A loan is said to be amortized when it is repaid by equal payments over a period of time. Though each payment of equal amount, the distribution between interest payment and principal repayment changes over time.

Answer and Explanation:

The interest for the 16th year is $2,850.55.

We can use the following formula to compute the monthly payment for a loan with principal {eq}P {/eq}, periodic interest rate {eq}r{/eq} and number of payments {eq}T{/eq}:

  • {eq}\displaystyle \frac{Pr}{1 - (1 + r)^{-T}} {/eq}

Applying the formula, the annual payment is:

  • {eq}\displaystyle \frac{100,000*5.5\%}{1 - (1 + 5.5\%)^{-25}} = 7454.93 {/eq}

To find the interest for the 16th year, we need to first compute the remaining balance, which is the present value of the remaining annual payments. In the 16th year, there are 25 - 16 = 9 annual payments. The present value of the remaining payments is:

  • {eq}\displaystyle \frac{7454.93*(1 - (1 + 5.5\%)^{-9})}{5.5\%} = 51,828.16 {/eq}

The interest payment = outstanding balance * interest rate = 51,828.16 * 5.5% = 2,850.55.


Learn more about this topic:

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Calculating Monthly Loan Payments

from Remedial Algebra I

Chapter 25 / Lesson 8
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