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Annual % Rate calculation
Using the nominal rate for a loan, is there a formula in Excel for
calculating the APR? Thanks and regards, PJF |
#2
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Annual % Rate calculation
"PJF" wrote:
Using the nominal rate for a loan, is there a formula in Excel for calculating the APR? That depends on how you define "APR" for a loan. For US loans conforming to the Truth In Lending regulation, the APR __is__ a "nominal" (non-compounded) annual rate. So the APR is the (nominal) annual interest rate, ignoring closing costs and monthly service fees like PMI. What distinguishes the APR from the annual interest rate is the inclusion of specific fees in the cost of the loan, typically the so-called "points" and most other closing costs, as well as PMI and any other monthly service charges, if any. See http://banking.about.com/od/loans/a/calculateapr.htm , among others. Suppose you have a 15-year fixed-rate loan of $100,000 paid off monthly at 6% with closing costs of 1% points and $1500 in additional "finance charges". The nominal monthly payment (excluding PMI and other monthly service charges) is computed the normal way, based on the full loan amount, to wit: =ROUNDUP(PMT(6%/12, 15*12, -100000), 2) Note that PMT must be rounded to some multiple of legal currency. I chose cents; a lender might choose dollars or any other unit. I chose to round up; thus, the last payment is no more than the regular payment. A lender might choose to round down; but in that case, the lender should disclose the amount of the last payment, if it is substantially different. The APR can be estimated using the nominal monthly payment and the loan amount less qualifying closing costs, to wit: =12 * RATE(15*12, monthlyPayment + PMI + otherServiceCharges, -(100000*(1-1%) - 1500)) This is only an estimate because the last nominal payment is different from the regular monthly payment computed with PMT above. Note: Minor adjustments must be made for different payment frequencies. Major adjustments must be made for loan structures that differ from US loans, notably Canada and perhaps the UK. |
#3
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Annual % Rate calculation
Joel,
Thanks so much for your detailed explanation. I appreciate the time you took to spell it out so thoroughly. Regards. PJF "JoeU2004" wrote in message ... "PJF" wrote: Using the nominal rate for a loan, is there a formula in Excel for calculating the APR? That depends on how you define "APR" for a loan. For US loans conforming to the Truth In Lending regulation, the APR __is__ a "nominal" (non-compounded) annual rate. So the APR is the (nominal) annual interest rate, ignoring closing costs and monthly service fees like PMI. What distinguishes the APR from the annual interest rate is the inclusion of specific fees in the cost of the loan, typically the so-called "points" and most other closing costs, as well as PMI and any other monthly service charges, if any. See http://banking.about.com/od/loans/a/calculateapr.htm , among others. Suppose you have a 15-year fixed-rate loan of $100,000 paid off monthly at 6% with closing costs of 1% points and $1500 in additional "finance charges". The nominal monthly payment (excluding PMI and other monthly service charges) is computed the normal way, based on the full loan amount, to wit: =ROUNDUP(PMT(6%/12, 15*12, -100000), 2) Note that PMT must be rounded to some multiple of legal currency. I chose cents; a lender might choose dollars or any other unit. I chose to round up; thus, the last payment is no more than the regular payment. A lender might choose to round down; but in that case, the lender should disclose the amount of the last payment, if it is substantially different. The APR can be estimated using the nominal monthly payment and the loan amount less qualifying closing costs, to wit: =12 * RATE(15*12, monthlyPayment + PMI + otherServiceCharges, -(100000*(1-1%) - 1500)) This is only an estimate because the last nominal payment is different from the regular monthly payment computed with PMT above. Note: Minor adjustments must be made for different payment frequencies. Major adjustments must be made for loan structures that differ from US loans, notably Canada and perhaps the UK. |
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