Question

A person purchased a ​$133,748 home 10 years ago by paying 20​% down and signing a​ 30-year mortgage at 10.2​% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 20​-year mortgage at 6.3 % compounded monthly. How much interest will refinancing​ save?

Money​ Saved: ​(Round to the nearest cent as​ needed.)

Answer 1

EMI :

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

Loan = Price ( 1 - Downpayment Ratio )

= $ 133748 ( 1 - 0.20 )

= $ 133748 * 0.8

= $ 106998.40

EMI = Loan / PVAF (r%, n)
= $ 106998.40 / PVAF (0.85%, 360)

= $ 106998.40 / 112.0591

= $ 954.84

Outstanding Bal after 10 Years:

Month	Opening bal	Instalment	Int	Principal Repay	Clsoing Bal
115	$    98,330.45	$ 954.84	$ 835.81	$ 119.03	$    98,211.42
116	$    98,211.42	$ 954.84	$ 834.80	$ 120.04	$    98,091.38
117	$    98,091.38	$ 954.84	$ 833.78	$ 121.06	$    97,970.32
118	$    97,970.32	$ 954.84	$ 832.75	$ 122.09	$    97,848.22
119	$    97,848.22	$ 954.84	$ 831.71	$ 123.13	$    97,725.09
120	$    97,725.09	$ 954.84	$ 830.66	$ 124.18	$    97,600.92
121	$    97,600.92	$ 954.84	$ 829.61	$ 125.23	$    97,475.69
122	$    97,475.69	$ 954.84	$ 828.54	$ 126.30	$    97,349.39
123	$    97,349.39	$ 954.84	$ 827.47	$ 127.37	$    97,222.02
124	$    97,222.02	$ 954.84	$ 826.39	$ 128.45	$    97,093.57
125	$    97,093.57	$ 954.84	$ 825.30	$ 129.54	$    96,964.02

Int for Balance 20 Years:

= Amount to be Paid - Outstsanding Balance

= [ 954.84 * 240 ] - [ 97600.92 ]

= $ 229161.44 - 97600.92

= $ 131560.52

New EMI:

EMI = Loan / PVAF (r%, n)
= $ 97600.92 / PVAF (0.525%,240)

= 97600.92 / 136.2685

= $ 716.24

Int = [Amount tobe Paid ] - Loan

= [ 716.24 * 240 ] - 97600.92

= 171897.6 - 97600.92

= 74296.65

Int Saved = $ 131560.52 - $ 74296.65

= $ 57263.87

Pls do rate, if the answer is correct and comment, if any further assistance is required.