Question

You want to buy a new sports car for $88,500. Tthe finance office at the dealership has quoted you an APR of 7% for 72 month loan to buy the car.

1. what will your monthly payments be?

2. what is the effective annual rate on this loan?

Answer 1

Part 1:

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	$             88,500.00
Int rate per Month	0.5833%
No. of Months	72

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 88500 / PVAF (0.0058 , 72)
= $ 88500 / 58.6544
= $ 1508.84

Part 2:

Effective Annual Rate = ( 1 + r ) ^ n - 1
r = Int Rate per period
n = No.of periods per anum

Particulars	Amount
Ret period	0.5833%
No. of periods	12.0000

EAR = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.005833 ) ^ 12 ] - 1
= [ ( 1.005833 ) ^ 12 ] - 1
= [ 1.0723 ] - 1
= 0.0723
I.e EAR is 7.23 %