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| In [[banking]] and [[finance]], an '''amortizing loan''' is a loan where the [[principal sum|principal]] of the loan is paid down over the life of the loan (that is, [[amortization|amortized]]) according to some [[amortization schedule]], typically through equal payments.
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| Similarly, an '''amortizing bond''' is a [[Bond (finance)|bond]] that repays part of the principal ([[face value]]) along with the [[coupon (bond)|coupon]] payments. Compare with a [[sinking fund]], which amortizes the total debt outstanding by repurchasing some bonds.
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| Each payment to the lender will consist of a portion of interest and a portion of principal. [[Mortgage loan]]s are typically amortizing loans. The calculations for an amortizing loan are those of an [[Annuity (finance theory)|annuity]] using the [[time value of money]] formulas, and can be done using an [[amortization calculator]].
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| An amortizing loan should be contrasted with a [[bullet loan]], where a large portion of the loan will be paid at the final maturity date instead of being paid down gradually over the loan's life.
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| An '''accumulated amortization loan''' represents the amount of amortization expense that has been claimed since the acquisition of the asset.
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| ==Effects==
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| Amortization of debt has two major effects:
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| ;Credit risk: First and most importantly, it substantially reduces the [[credit risk]] of the loan or bond. In a [[bullet loan]] (or [[bullet bond]]), the bulk of the credit risk is in the repayment of the principal at maturity, at which point the debt must either be paid off in full or rolled over. By paying off the principal over time, this risk is mitigated.
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| ;Interest rate risk: A secondary effect is that amortization reduces the [[Bond duration|duration]] of the debt, reducing the debt's sensitivity to [[interest rate risk]], as compared to debt with the same [[Maturity (finance)|maturity]] and [[coupon rate]]. This is because there are smaller payments in the future, so the weighted-average maturity of the cash flows is lower.
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| ==Weighted-average life==
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| {{main|Weighted-average life}}
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| The number [[weighted average]] of the times of the principal repayments of an amortizing loan is referred to as the [[weighted-average life]] (WAL), also called "average life". It's the average time until a dollar of principal is repaid.
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| In a formula,
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| :<math>\text{WAL} = \sum_{i=1}^n \frac {P_i}{P} t_i,</math>
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| where:
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| * <math>P</math> is the principal,
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| * <math>P_i</math> is the principal repayment in coupon <math>i</math>, hence
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| * <math>\frac{P_i}{P}</math> is the fraction of the principal repaid in coupon <math>i</math>, and
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| * <math>t_i</math> is the time from the start to coupon <math>i</math>.
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| ==See also==
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| * [[Amortization calculator]]
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| * [[Amortization schedule]]
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| * [[Amortization (business)]]
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| * [[Sinking fund]]
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| * [[Weighted-Average Life]]
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| ==References==
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| {{reflist}}
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| [[Category:Debt]]
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| [[Category:Bonds (finance)]]
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| [[Category:Loans]]
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