Question

1. Derek borrows $263,106.00 to buy a house. He has a 30-year mortgage with a rate of 4.65%. After making 113.00 payments, how much does he owe on the mortgage?

2. Derek borrows $36,439.00 to buy a car. He will make monthly payments for 6 years. The car loan has an interest rate of 5.76%. What will the payments be?

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	$          263,106.00
Int rate per Month	0.3875%
No. of Months	360

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 263106 / PVAF (0.0039 , 360)
= $ 263106 / 193.935
= $ 1356.67

Loan Outstanding after 113 Months:

Particulars	Amount
Loan Amount	$ 263,106.00
Int rate per Month	0.3875%
No. of Months	360
Outstanding Bal after	113
EMI	$      1,356.67
Payments Left	247

Outstanding Bal = Instalment * [ 1 - ( 1 + r )^ - n ] / r
= $ 1356.67 * [ 1 - ( 1 + 0.003875 ) ^ - 247 ] / 0.003875
= $ 1356.67 * [ 1 - ( 1.003875 ) ^ - 247 ] / 0.003875
= $ 1356.67 * [ 1 - 0.384706 ] / 0.003875
= $ 1356.67 * [ 0.615294 ] / 0.003875
= $ 215419.59

Loan outstanding after 113 period is $ 215,419.74

r = Int Rate per period
n = Balance No. of periods
Loa

Part 2:

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	$             36,439.00
Int rate per Month	0.4800%
No. of Months	72

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 36439 / PVAF (0.0048 , 72)
= $ 36439 / 60.754
= $ 599.78

Monthly payment is $ 599.78