Question

The Taylors have purchased a $250,000 house. They made an initial down payment of $10,000 and secured a mortgage with interest charged at the rate of 8%/year on the unpaid balance. Interest computations are made at the end of each month. If the loan is to be amortized over 30 years, what monthly payment will the Taylors be required to make? (Round your answer to the nearest cent.)
$ ________

What is their equity (disregarding appreciation) after 5 years? After 10 years? After 20 years? (Round your answers to the nearest cent.)

5 years	$
10 years	$
20 years	$

Answer 1

Part A:

Price = $ 250000

Down Payment = $ 10000

Loan = $ 250000 - $ 10000 I.e $ 240000

Particulars	Amount
Loan Amount	$         2,40,000.00
Int rate per Month	0.6667%
No. of Months	360

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 240000 / PVAF (0.0067 , 360)
= $ 240000 / 136.2835
= $ 1761.03

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

Part B:

After 5 Years:

Equity = Asset - Liability

Liability = Loan Outstanding

Loan Outstanding:

Particulars	Amount
Loan Amount	$ 2,40,000.00
Int rate per Month	0.6667%
No. of Months	360
Outstanding Bal after	60
EMI	$      1,761.03
Payments Left	300

Outstanding Bal = Instalment * [ 1 - ( 1 + r )^ - n ] / r
= $ 1761.03 * [ 1 - ( 1 + 0.006667 ) ^ - 300 ] / 0.006667
= $ 1761.03 * [ 1 - ( 1.006667 ) ^ - 300 ] / 0.006667
= $ 1761.03 * [ 1 - 0.136237 ] / 0.006667
= $ 1761.03 * [ 0.863763 ] / 0.006667
= $ 228155.48

r = Int Rate per period
n = Balance No. of periods
Equity = $ 250000 - $ 228155.48

= $ 21844.52

After 10 Years:

Particulars	Amount
Loan Amount	$ 2,40,000.00
Int rate per Month	0.6667%
No. of Months	360
Outstanding Bal after	120
EMI	$      1,761.03
Payments Left	240

Outstanding Bal = Instalment * [ 1 - ( 1 + r )^ - n ] / r
= $ 1761.03 * [ 1 - ( 1 + 0.006667 ) ^ - 240 ] / 0.006667
= $ 1761.03 * [ 1 - ( 1.006667 ) ^ - 240 ] / 0.006667
= $ 1761.03 * [ 1 - 0.202971 ] / 0.006667
= $ 1761.03 * [ 0.797029 ] / 0.006667
= $ 210528.27

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

Equity = $ 250000 - $ 210528.27

= $ 39471.73

AFter 20 Years:

Particulars	Amount
Loan Amount	$ 2,40,000.00
Int rate per Month	0.6667%
No. of Months	360
Outstanding Bal after	240
EMI	$      1,761.03
Payments Left	120

Outstanding Bal = Instalment * [ 1 - ( 1 + r )^ - n ] / r
= $ 1761.03 * [ 1 - ( 1 + 0.006667 ) ^ - 120 ] / 0.006667
= $ 1761.03 * [ 1 - ( 1.006667 ) ^ - 120 ] / 0.006667
= $ 1761.03 * [ 1 - 0.450523 ] / 0.006667
= $ 1761.03 * [ 0.549477 ] / 0.006667
= $ 145139.57

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

Equity = $ 250000 - $ 145139.57

= $ 104860.43