Question

Susan bought a home with a sale price of $235,000. She put down 20%, and obtained a loan for the balance. Her interest rate was 7% and the term was thirty years. Her monthly payment included principal and interest, taxes of $208.33 and insurance of $109. The total payment was $1,568.10. How much will she owe on the principal balance of the loan after the second month's payment has been made?

Answer 1

Answer:

Given Data:

Selling price = $235,000

Down Payment = 20% of Selling Price

I = Interest Rate (yearly) = 7%

i = Interest Rate (monthly) = 0.583%

n = Term of Payment = 3 years = 360 months

Taxes (monthly) = $208.33

Insurance (monthly) = $109

Total Payment (monthly) = $1,568.10

Explanation:

As 20% of the selling price is already paid upfront. The principal amount can be obtained as follows:

P = Principal Amount = 235,000 - (235,000 * 20%)

P = Principal Amount = $188,000

Monthly Payment will be,

M = Monthly Payment = Total Payment - Tax - Insurance

M = Monthly Payment = 1568.10 - 208.33 -109

M = Monthly Payment = 1250.77 = $ 1251

Initial interest payment can be calculated by,

Interest (1st month) = Principal Amount * $(\frac{Interest\; Rate}{12})$

Interest = 188000 * $(\frac{7\%}{12})$

Interest = $1097

Now let us calculate the amount of principal remaining (R) after 2  months.

$R\; =\; \frac{1}{i}\;*\;[M\;+\;(1\;+\;i)^x\;*\;(P*i-M)]\\\\where\;=\;2\;(months),\\\\\therefore R\; =\; [1251\;+\;(1\;+\;0.00583)^2\;*\;(188000*0.00583-1251)]\;*\;\frac{1}{0.00583}$

R = $187690.43