Question

You want to buy a car, and a local bank will lend you $10,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 8% with interest paid monthly. What will be the monthly loan payment? What will be the loan's EAR? Do not round intermediate calculations. Round your answer for the monthly loan payment to the nearest cent and for EAR to two decimal places.

Answer 1

Part A:

EMI :
EMI or Instalment is sum of money due as one of several equal payments for loan/ Mortgage taken today, spread over an agreed period of time.

EMI = Loan / PVAF (r%, n)
PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

How to calculate PVAF using Excel:
=PV(Rate,NPER,-1)
Rate = Disc Rate
NPER = No.of periods

Particulars	Amount
Loan Amount	$             10,000.00
Int rate per Month	0.6667%
No. of Months	60

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 10000 / PVAF (0.0067 , 60)
= $ 10000 / 49.3184
= $ 202.76

Part B:

Particulars	Amount
Ret period	0.6667%
No. of periods	12.0000

Effective Annual Return = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.006667 ) ^ 12 ] - 1
= [ ( 1.006667 ) ^ 12 ] - 1
= [ 1.083 ] - 1
= 0.083
I.e EAR is 8.3 %