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Consider a standard mortgage (360 months) with monthly payments and a nominal rate (monthly...

Question:

Consider a standard mortgage (360 months) with monthly payments and a nominal rate (monthly compounding) of 5.10%. What portion of the payments during the first 28 months goes toward principal?

Loan amortization:

Loan amortization refers to the repayment of a loan in installments at a specified interest rate. Each payment settles the accrued interest rate for the period and partly repay the principal amount.

Answer and Explanation:

About 3.5% of the first 28 payments goes toward principal.

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

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

Applying the formula, the monthly payment, denote by {eq}M{/eq} is:

  • {eq}M = \displaystyle \frac{P*5.1\%/12}{1 - (1 + 5.1\%/12)^{-360}} = 0.005429497734* P {/eq}

Next, we need to compute the amount of the remaining balance, which is the present value of the remaining 332 payments, i.e.,

  • {eq}\displaystyle \frac{M(1 - (1 +5.1\%/12)^{-332})}{5.1\%/12} = 177.7342143*M \\ = 177.7342143 *(0.005429497734* P)\\ = 0.9650075139* P{/eq}

Therefore, the principal portion of the payment during the first 28 payments is:

  • {eq}\displaystyle \frac{P - 0.9650075139* P}{P} = 0.03499248614 = 3.5\%{/eq}

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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