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In: Finance

Sarah purchased a condo for $200,000 with a $45,000 down payment and a $155,000 bank loan....

Sarah purchased a condo for $200,000 with a $45,000 down payment and a $155,000 bank loan. The mortgage is to be amortized in just 15 years with an interest rate of 3% per year, compounded monthly. 10 years later, the value of her condo has risen to $260,000 and she would like to sell her property. How much does she still owe on her mortgage? What is her equity in the condo at this point?

Please show your work and formula. Step by step.

Thank you

Expert Solution

Given the purchased value of Condo = $200,000

Down Payment = $45,000

Amount of the loan is 1,55,000.

The formula for calculating the monthly equalised installments is.

[P x R x (1+R)^N]/[(1+R)^N-1], where P stands for the loan amount or principal, R is the interest rate per month

Given the interest rate is 3% compounded monthly now the monthly interest rate is calculated as follows

Let X be the monthly interest rate, Hence

(1+X)^12 = 1.03

X = 0.002466 nothing but 0.246627%

Hence the monthly installment is

155000 * 0.002466 *(1.002466)^15*12/((1.002466)^15*12-1)

= 155000 * 0.002466 * 1.557967/0.557967

= 1067.387

Market value of Condo - Mortage payment remaining = $2,60,000 - 59457.83 = 200542.2 .Hence she still owes 59,457.83 to the bank and the equity value will be
Balance at the end of year -10 as seen from the schedule is 59457.83

Note - I have presented the amortization schedule for year-1 and at year -10 ,that is at 120th month,similarly this format can be used to draw the schedule for 180 months. I am unable to paste it here due to words constraint.

Month	Opening Principal	Interest	Installment	Closing Principal
1	1,55,000.00	382.23	1,067.39	1,54,314.84
2	1,54,314.84	380.54	1,067.39	1,53,628.00
3	1,53,628.00	378.85	1,067.39	1,52,939.46
4	1,52,939.46	377.15	1,067.39	1,52,249.22
5	1,52,249.22	375.45	1,067.39	1,51,557.28
6	1,51,557.28	373.74	1,067.39	1,50,863.63
7	1,50,863.63	372.03	1,067.39	1,50,168.27
8	1,50,168.27	370.31	1,067.39	1,49,471.20
9	1,49,471.20	368.60	1,067.39	1,48,772.41
10	1,48,772.41	366.87	1,067.39	1,48,071.90
11	1,48,071.90	365.15	1,067.39	1,47,369.65
12	1,47,369.65	363.41	1,067.39	1,46,665.68

Month	Opening Principal	Interest	Installment	Closing Principal
109	70,331.91	173.44	1,067.39	69,437.97
110	69,437.97	171.23	1,067.39	68,541.81
111	68,541.81	169.02	1,067.39	67,643.45
112	67,643.45	166.81	1,067.39	66,742.87
113	66,742.87	164.59	1,067.39	65,840.07
114	65,840.07	162.36	1,067.39	64,935.05
115	64,935.05	160.13	1,067.39	64,027.79
116	64,027.79	157.89	1,067.39	63,118.30
117	63,118.30	155.65	1,067.39	62,206.56
118	62,206.56	153.40	1,067.39	61,292.57
119	61,292.57	151.15	1,067.39	60,376.33
120	60,376.33	148.89	1,067.39	59,457.83

jeff jeffy answered 2 years ago

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