Question

Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) (Round your answer to the nearest cent.)

1. A $100,000, 35-year, 4.5% mortgage after 10 years

2. A $450,000, 20-year, 3.2% mortgage after 15 years

Answer 1

Part 1:

Particulars	Amount
Loan Amount	$         1,00,000.00
Int rate per Month	0.3750%
No. of Months	420

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 100000 / PVAF (0.0038 , 420)
= $ 100000 / 211.3018
= $ 473.26

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	$ 1,00,000.00
Int rate per Month	0.3750%
No. of Months	420
Outstanding Bal after	120
EMI	$         473.26
Payments Left	300

Outstanding Bal = EMI * [ 1 - ( 1 + r )^ - n ] / r
= $ 473.26 * [ 1 - ( 1 + 0.00375 ) ^ - 300 ] / 0.00375
= $ 473.26 * [ 1 - ( 1.00375 ) ^ - 300 ] / 0.00375
= $ 473.26 * [ 1 - 0.325336 ] / 0.00375
= $ 473.26 * [ 0.674664 ] / 0.00375
= $ 85144.4

r = Int Rate per period
n = Balance No. of periods
Actual Answer is $ 85143.77 Difference is due to Rounding off Problem

Part 2:

Particulars	Amount
Loan Amount	$         4,50,000.00
Int rate per Month	0.2667%
No. of Months	240

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 450000 / PVAF (0.0027 , 240)
= $ 450000 / 177.0968
= $ 2540.98

Particulars	Amount
Loan Amount	$ 4,50,000.00
Int rate per Month	0.2667%
No. of Months	240
Outstanding Bal after	180
EMI	$      2,540.98
Payments Left	60

Outstanding Bal = Instalment * [ 1 - ( 1 + r )^ - n ] / r
= $ 2540.98 * [ 1 - ( 1 + 0.002667 ) ^ - 60 ] / 0.002667
= $ 2540.98 * [ 1 - ( 1.002667 ) ^ - 60 ] / 0.002667
= $ 2540.98 * [ 1 - 0.852325 ] / 0.002667
= $ 2540.98 * [ 0.147675 ] / 0.002667
= $ 140697.12

Actual Answer is 140714.60. Difference is due to Rounding off Problem

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