Auto Loan Payment Example

Problem

A car is financed using a three-year loan. The loan has a 8% nominal annual interest rate, compounded monthly. The price of the car is 7,000, and a deposit of 2,000 is paid in cash. Calculate the monthly auto loan payments, assuming that the payments start one month after the purchase.

Solution

The value of the loan is the price of the car less the initial deposit (7,000 – 2,000 = 5,000) (PV). This loan is repaid using monthly installments, so one period is one month, and the term of the loan is 3 years or 36 months (n). The interest rate has been quoted as an annual rate so the periodic (monthly) rate is 8%/12 per month (i)

As the auto loan payments (Pmt) are made at the end of each period, and we know the present value, the problem is solved using the annuity payment formula PV as follows:

Auto loan payment = PV x i / (1 - 1 / (1 + i)n)
PV = Value of the auto loan 5,000
n = number of months = 3 x 12 = 36
i = nominal rate = 8%/12 per month
Auto loan payment = 5000 x (8%/12) / (1 - 1 / (1 + 8%/12)36)
Auto loan payment = 156.68 

Auto Loan Payment Explanation

For the auto loan balance to be cleared at the end of 36 payments, the present value of the payments must be equal to the present value of the auto loan.

The solution to this problem simply uses the present value of an annuity formula to find the 36 payments which, at a discount rate of 8%/12, will give a present value of the auto loan of 5,000.

Auto Loan Payment Example November 6th, 2016Team

You May Also Like


Related pages


debit note definition accountingdebtors collection period ratio analysissales ledger control account reconciliationformula for calculating markup percentageaccounting entry for retained earningscost accounting conceptsproject payback period calculatorlifo vs fifo exampleexcel pmt function formulageneral ledger accounts receivablepurchased goods on credit journal entriesmark up calculatordirect material cost variance formulainterest accrualsexcel basics quizprepayments journal entryimprestdouble declining balance exampleaccrual to cash basis conversiontrade accounts receivable definitionformula growing annuitypetty cash reconciliation templateis prepaid rent an assetpv of a lump sumbookkeeping testsbad debt reserve journal entrypresent value of lump sum tablewhat accounts are affected by closing entriesbalance sheet excel templatecumulative prefered stockvoucher layoutmargin and markup formulareconcile retained earningspetty cash in balance sheetcost accounting excel templateshow to figure out contribution marginwhat is amortisation in accountingbookkeeping samplevacation accrual formulaworksheet examples accountinginventory adjusting entrydouble entry bookkeeping tutorialwhat is a trade debtor on the balance sheetsales ledger accountcredit note issued by supplierwhat is intangible assets examplespayroll entries general ledgerfifo calculationsimprest formpresent value annuity tablesprove it data entry practice testbad debt expense on balance sheetcash imprest systemannuity formulfuture value annuity due calculatoradjusted trial balance worksheet templateerrors in bank reconciliation statementcontra entry meaning with exampleallowance for doubtful debts in balance sheetroce ratioaccruals and prepayments practice questionsjob costing excel templatepmt function calculatorhow do you calculate retained earningswhat are consumable suppliespresent value of lump sumexamples of accruals in accountingtrial balance meaning in accountingmeaning of operating cycleretail markup formulaacceptable gearing ratiopremium bonds repaymenthow to calculate number of days sales in receivablesinventory perpetual methodjournal entry to record accounts payablegoods receipt noteexample of overstatementnominal annual rate of return calculatorrequisition of materialsshort term notes payable definitionsale of fixed asset journal entrypayment voucher sample format