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Appendix D: Amortization Formulas The example of an amortization schedule from the Financing subsection of Section 2 of this manual follows: Abusinessborrows$10,000at10%compoundedmuallytoberepaidin5years. Theannualpayment due to the lender can be calculated by multiplying the uniform capital recovery factor--(UCRF= [d(l + d)"]/[(l + d>"- 11)--by the amount borrowed. In this example, UCRF equals [O.l(l + 0.1)5]/[(l+0.1)5- 11=0.2638,whichwhenmultipliedbythe$10,000amountborrowedgivesauniform annual payment to the lender of $2,637.97. Table I>-I illustrates the amortization schedule for this example. Year 0 1$ 2 3 4 5 2,637.97 2,637.97 2,637.97 2,637.97 2,637.97 239.82 $ 3,189.87 Table D-I (1') Annual Payment (I x UCRF) Amortization Schedule Used for Example (2) Interest (d x C01.4("")) $ 1,000.08 836.20 656.03 457.a3 RP,=Ix(1-[(UCW, -i)/(UCRF, -i)]} = principal remaining after the mthpayment (4) Principal Balance (COf.4(""')- CoI.3) $ 10,000.00 8,362.03 6,560.25 4,578.30 2,398.16 0.00 $ 13,189.87 The formula for calculating the principal remaining after each period follows. Totals Where: RPrn $ 10,000.00 I = UCRFy = UCRF, = i = initial investment or amount borrowed uniform capital recovery factor [d(l +d)']/[(l +d)' -11, where the discount rate is equal to the rate of interest (i) and the parameter y is equal to the term of the loan uniform capital recovery factor [d(l + d)m]/[(l + d)m-11, where the discount rate is equal to the rate of interest (i) and the parameter m is equal to the year for which the remaining principal is being calculated interest rate of loan. The formula for calculating the portion of interest contained in a specific payment is simple and can be calculated using the same formula for calculating the remaining principal. In the formula, UCRFmis simply replaced by UCRF,-, to arrive at the principal remaining in the period prior to the one under examination. Once the remaining principal from the prior period is calculated, it can be multiplied by the interest rate (i) to arrive at the interest portion of the payment. D-1 (3) Repayment of Principal (C0l.l - C01.2) $ 1,637.97 1,801-77 1,981.95 2,180.14 2,398.16 (D-1)PDF Image | A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies
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